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Step 1
Combine flour and salt in the bowl of a stand mixer. Make a well in the center. Pour the whole eggs, yolks, and 1 tsp olive oil into the well and whisk with a fork, gradually incorporating more flour in from the sides until you have a very thick, wet mixture in the middle.
Step 2
Attach the dough hook and run the machine on low, pausing occasionally to push more flour from the sides into the center.
Step 3
Once the dough comes together in a shaggy mass and there's no loose flour left in the bottom of the bowl (add the extra 1 tsp olive oil to the dry bits if they're not getting incorporated), up the speed to medium low and knead on low until the dough is smooth, about 6-8 minutes. It will feel quite stiff.
Step 4
Wrap the dough in plastic and let chill in the fridge for at least 30 minutes, or up to 24 hours before use.
Step 5
Drain the ricotta: Line a quarter sheet pan with two layers of paper towels. Spread the ricotta in a thin layer and cover with two more layers of paper towels, pressing them gently onto the surface of the cheese. Let sit for 5 minutes.
Step 6
Toast the walnuts: Arrange whole walnuts on a sheet pan and toast in a 300°F oven for 15-20 minutes until well browned, giving the pan a shake every 5 minutes or so. Remove from the oven. Once cool, finely chop them and set aside.
Step 7
Blend the cheeses: Combine the drained ricotta, gorgonzola cheese, salt, and pepper in the bowl of a mini food processor. Process on low just to combine and to break up the larger gorgonzola crumbles.
Step 8
Stir together cheeses, finely chopped walnuts, minced apple (tossed with a squeeze of lemon juice to prevent browning) in a medium bowl. Adjust salt and pepper to taste. Cover and chill until ready to use.
Step 9
Divide pasta dough in half. Keep dough you aren't using wrapped until ready to use.
Step 10
Roll pasta dough to a "6" thinness using a pasta roller, starting with the widest setting on the roller. Roll the dough through twice on each setting so that it fully relaxes and doesn't shrink back. Dust with flour as needed to prevent sticking.
Step 11
Lightly dust a clean countertop with flour and lay out the sheet of dough. Trim ends where they're lopsided so you have a clean rectangle.
Step 12
Fold the dough in half lengthwise (so if it was 20"x5" it would now be 10"x5"). Unfold and cut where the crease was so that you have two equal sized sheets of pasta.
Step 13
Dust additional flour under the sheet that will form the bottom of your ravioli so it doesn't stick to the counter. Use a pastry brush or dry paper towel to brush and excess flour off the surface of the pasta sheet.
Step 14
Without cutting all the way through the pasta, use your ravioli stamp to lightly mark two rows of ravioli so you know where to place the filling. If using a circle cutter, leave about ¾-1" between each; If you're using a square ravioli cutter they can be much closer together or not have any gap at all.
Step 15
Scoop 1½ tsp of filling into the center of each ravioli.
Step 16
Lay the other sheet of pasta over the filling. Working from the center outward, use your fingers to gentle smooth out the dough and seal the two layers together around the mounds of filling. Seal the outer edges of the pasta sheet last so to avoid trapping air bubbles.
Step 17
Carefully place your ravioli stamp over each mound of filling and press down firmly to cut through the pasta and seal the edges shut.
Step 18
Pull up any excess dough and knead or combine together to re-roll later.
Step 19
Gently pull ravioli up off the counter (use a bench scraper or thin metal spatula if they're sticking) and transfer to a lightly floured sheet pan to dry or cook immediately.
Step 20
Bring a pot of salted water to a rolling boil, then reduce to a simmer. Cook fresh ravioli for 3 minutes (4 minutes if they've dried slightly) without crowding the pan.
Step 21
Serve with brown butter and a drizzle of balsamic vinegar.