Step 1

For the apple puree: Peel, core, and chop the apples into 1/2-inch pieces.

Step 2

In a small pot, combine apple, 1 1/2 tablespoons lemon juice, light brown sugar, honey, and a pinch of sea salt. Cook over medium-low heat, stirring occasionally, until the apples become translucent and soft, and the liquid has almost totally evaporated, about 15 to 20 minutes.

Step 3

Use an immersion blender (or transfer to a food-processor,) and pulse until the apples are mostly pureed, but not completely smooth.

Step 4

Transfer to a bowl and place in the freezer to flash-chill until cold, about 1 hour, stirring it every 15 minutes speeds up the process. (Alternatively, make the puree up to 24 hours in advance and chill, covered, in the refrigerator until ready to use.)

Step 5

For the vanilla custard: In a small pot, whisk together the milk, vanilla bean scrapings, egg yolks, granulated sugar, and flour until completely smooth (puree in a blender or in the pot with an immersion blender to expedite this process). Cook the mixture over medium-low heat, stirring constantly, until it starts to thicken and bubbles slowly form on the surface, about 15 minutes. Turn off heat immediately, then stir in butter, remaining 1/4 teaspoon lemon juice, and a pinch of sea salt until the custard is silky and smooth.

Step 6

Transfer to a bowl and cover with plastic wrap that directly touches the surface of the custard (to prevent a skin from forming). Place in the freezer to flash-chill until cold, about 1 hour (stirring it every 15 minutes speeds up the process. (Alternatively, make the puree up to 24 hours in advance and chill, covered, in the refrigerator until ready to use.

Step 7

For the pastry dough: In a large bowl, combine flour, sea salt and water, and mix until a craggy but even and cohesive dough forms (it should look somewhere in between shaggy pie dough and smooth brioche dough). Resist the urge to knead it further—we don't want much gluten to develop. Lightly flour the dough and wrap it in parchment, then place in the freezer to flash-chill for until the dough is cool to the touch, about 15 minutes.

Step 8

Transfer the chilled dough onto a well-floured work surface and roll it out into a rectangle about 8x11-inch. Evenly arrange the sliced butter to cover the bottom two-thirds of the rectangular dough, leaving about a 3/4-inch border all around. Working quickly (especially if it’s warm in your kitchen, as the butter will soften fast,) brush some of the beaten egg over the margin.

Step 9

Fold the dough like an envelope: fold the exposed top third halfway over the buttered area. Gently smooth the folded area to eliminate any big air pockets, then fold the bottom, buttered third of the dough over so you’re left with a rectangle roughly 8x3 2/3-inches. Gently smooth out air pockets then pinch outer edges of the dough together to make sure they’re sealed. Trim any excess edges for a neater dough-envelope.

Step 10

Rotate the dough 90 degrees, dust with just a bit of flour if the dough is sticking, then roll it out into another 8x11-inch rectangle. (This would only happen if the temperature in the room is warm, but some butter may squeeze out from the edges but don’t panic, simply smear it back onto the dough wherever, dust with a bit more flour, and keep rolling. If any large air bubbles surface, poke them with a wooden skewer.)

Step 11

Dust the dough with more flour, then fold it like an envelope as you did in step Repeat step 4, then fold the dough like an envelope once more, for a total of three folds. Place the dough on a small sheet pan or plate and transfer to the freezer to chill for 15-20 minutes.

Step 12

Place the chilled dough on a lightly floured work surface, seam-side down, and roll out into a rectangle about 10x15-inches. Trim all the edges to make it a perfect rectangle.

Step 13

Spread the apple puree in the middle of the pastry, covering an area little more than one third, and leaving a 3/4-inch margin.

Step 14

Gently spread the vanilla custard on top of the apple puree in about a 3/4-inch layer (you may have extra left which is great for eating from a spoon).

Step 15

Brush more beaten egg around the margin, then fold the left and right sides of the dough towards the middle, and over the fillings (the dough should partially overlap). Pinch the top and bottom edges to seal tightly, then flip the whole thing over so the seam-side is down. Chill in the fridge while you preheat the oven (but no longer). Preheat the oven to 400°F (fan-on convection oven) or 425°F in a conventional oven.

Step 16

When ready to bake, brush the surface of the pastry with more beaten egg, and cut a few slits on the top to allow steam to escape. Bake for 35 min, rotating halfway, until golden-brown all over. Let cool on a rack for 20 minute before slicing.