Step 1

1 For the doughnuts: Warm the milk in a small saucepan over low heat, to 105 degrees

Step 2

2 Remove from the heat

Step 3

3 Sprinkle the yeast over the milk and add the water; let the mixture sit for about 15 minutes

Step 4

4 It will thicken

Step 5

5 Combine the flour, granulated sugar and salt in the bowl of a stand mixer fitted with a paddle attachment

Step 6

6 Add the yeast mixture, vanilla bean, eggs and egg yolks; beat on medium-low speed to form a shaggy mass with no visible dry ingredients

Step 7

7 Add the butter in three additions, waiting until each one is well blended before adding the next

Step 8

8 Beat until the dough looks somewhat smooth

Step 9

9 Switch to a dough-hook attachment

Step 10

10 Beat/knead on medium-low speed for 10 minutes; the dough should look smoother still, and most of it will gather around the dough hook

Step 11

11 To see whether gluten has developed, take a golf ball-size piece of dough and stretch it gently between your thumbs and first two fingers on both hands

Step 12

12 If it doesn’t break or tear and stretches enough to create a somewhat transparent swath of dough, it’s good to go

Step 13

13 If not, beat for another 5 minutes

Step 14

14 Grease a large bowl with cooking oil spray; scrape the dough into the bowl and cover with greased plastic wrap directly on the surface

Step 15

15 Let sit for 30 minutes, then fold over to smooth the surface

Step 16

16 Re-cover and refrigerate for 6 to 15 hours

Step 17

17 Uncover and transfer the dough to a floured work surface

Step 18

18 If you wish to make just one batch, divide the dough in half (best to weigh it) and place the rest in a freezer-safe gallon-size zip-top bag, sealing it as you press out any air

Step 19

19 Freeze for up to 2 months

Step 20

20 Flour the rolling pin

Step 21

21 Press down the dough on the work surface and roll into rectangle that’s about 9 by 10 1/2 inches; the slab should be about 1/2-inch thick

Step 22

22 Let it rest for 5 to 10 minutes

Step 23

23 Meanwhile, cut thirteen or fourteen 4-inch square pieces of parchment paper, then grease their tops lightly with cooking oil spray and arrange them on two baking sheets

Step 24

24 Use the 3-inch cutter or knife and ruler to cut 9 doughnuts, as close together as possible

Step 25

25 Use the small cutter to cut out the doughnut holes

Step 26

26 Place each doughnut on its own piece of parchment, and gather the holes on their own piece or two of parchment

Step 27

27 Gather together the scraps and re-roll to a thickness of 3/4 inch (thicker than the first roll); cut 3 more doughnuts and corresponding holes, placing them on the papers and baking sheet like before

Step 28

28 Cover with greased plastic wrap and let rise for at least 1 hour and up to 3 hours, in a draft-free spot; the doughnuts should almost double in height

Step 29

29 (If the doughnuts rise in a turned-off oven that had been preheated to 170 degrees, they will rise faster

Step 30

30 )

Step 31

31 Meanwhile, make the glaze: Combine the confectioners’ sugar, 1/2 cup of the hot water, the vanilla extract (yes, it really is that much!), salt and vanilla bean scrapings in the bowl of a stand mixer or handheld mixer; beat on medium speed until smooth, adding some or all of the remaining hot water, as needed, to form a thick glaze

Step 32

32 Cover with plastic wrap until ready to use

Step 33

33 Heat the oil in a wok over medium to medium-low heat (325 degrees)

Step 34

34 Working with two or three at a time, slide the doughnuts on their papers into the hot oil; use tongs to pluck out the papers, which should float free within seconds

Step 35

35 Flip the doughnuts right away; then turn them a total of four times over a total of 4 minutes, until golden brown and puffed

Step 36

36 Monitor the oil temperature and adjust the heat, as needed

Step 37

37 Use a Chinese skimmer to transfer the doughnuts to a wire rack set over paper towels to cool for 5 or 10 minutes

Step 38

38 When you're done with half of them, toss them one at a time into the bowl of glaze, turning to coat all over

Step 39

39 Place on a second wire rack, seated inside a rimmed baking sheet, until the glaze has set

Step 40

40 Repeat to fry the remaining doughnuts and holes; glaze the rest of the batch the same way

Step 41

41 SAVORY VARIATIONS: Instead of glazing the warm doughnuts or holes, dip them briefly in melted, unsalted butter then roll in grated Parmigiano-Reggiano cheese

Step 42

42 Pinch scraps or extra dough into walnut-size balls; dunk them in a mixture of extra-virgin olive oil and fresh chopped herbs (such as rosemary and thyme), then pack them loosely together in a greased baking dish — like monkey bread

Step 43

43 Drizzle more of the herbed olive oil on top and sprinkle with Parm

Step 44

44 Let them proof/rise for 20 to 30 minutes, then bake at 350 degrees for about 45 minutes; they're done when a tester inserted into the center comes out clean

Step 45

45 Serve warm

Step 46

46 Instead of coating the individual balls of dough in an herbed olive oil, bake them plain in a greased baking dish at 350 degrees for 25 minutes, then brush liberally with your favorite barbecue sauce

Step 47

47 Continue to bake for another 20 minutes, until browned and cooked through (use the same tester method for doneness)

Step 48

48 Serve warm, with more barbecue sauce for dipping