These donuts were inspired by the freshly fried donuts Chef Solomonov enjoys eating at the Jersey Shore boardwalk. Egg yolks, buttermilk, and melted butter make the cake rich and soft. Turning loose cake batter into donuts takes some skill (and lots of dusting flour!), but Solomonov is here to help you nail it.
Batter: In the bowl of a stand mixer fitted with a paddle attachment, add egg yolks and sugar. Mix on medium speed just to combine, then increase speed to medium-high and beat until mixture is pale and fluffy and ribbons start to form, about 3 minutes. Reduce to medium speed, then slowly stream in the melted butter, followed by the buttermilk; mix until combined, about 5 seconds.
Turn the mixer off. Add the dry ingredients: flour, baking soda, baking powder, salt and baharat. Mix on low speed just to combine, about 30 seconds. Increase speed to medium and continue mixing until dough is smooth and starts to pull away from the sides of the bowl, 20 to 30 seconds.
Tape a 12" x 16" sheet of parchment paper to your work surface to keep it from slipping. Generously dust the parchment with flour. (Keep extra flour nearby to use as needed.) Scrape down the paddle attachment, then turn all the batter out onto the floured surface. The batter will be very sticky and loose. Dust the top of the batter with more flour, all the way to the edges; flour your hands thoroughly. Place a second piece of parchment paper on top of the flour-dusted batter. Roll the batter between the parchment paper into a ½-inch thick rectangle, about 10" x 14". Using only the weight of the rolling pin itself, very gently ease it along the parchment paper—first from top to bottom, then from side to side—to evenly flatten the batter without rolling it too thin. Once you've achieved the right thickness, slide the dough (still sandwiched between parchment) onto an overturned baking sheet. Freeze for 30 minutes and up to overnight.
Preheat the frying oil: In a large, heavy-bottomed pot or Dutch oven over medium-high heat, add 2–3 inches of oil. Clip a deep fry thermometer onto the side of the pot and heat oil to 350 F. After at least 30 minutes, remove dough from freezer. Generously dust your work surface with flour. Peel the top layer of parchment off the dough. (It’s ok if some of it sticks—just be gentle and persistent!) Flip the baking sheet with dough onto the floured surface, so the bottom piece of parchment is now on top. Remove this layer of parchment and use a pastry brush to brush excess flour off dough.
Cut donuts: Use two sizes of ring cutters to quickly cut out the donuts. Flouring the cutters well and often to prevent sticking, stamp out as many 2.75-inch circles as possible; then use the 1-inch cutter for the holes. The dough scraps can be gathered together, re-rolled and cut for more donuts.
Fry the donuts: Carefully lift the dough rings with a spatula and slide them into the oil, frying about 4 at a time, depending on the size of your pot. After about 1 minute, the edges will begin to brown; flip the donuts and fry for another minute, then flip again and fry until golden brown and delightfully puffy, another 30 seconds. (Total frying time for the donuts will be about 2½ minutes.)Transfer donuts to a rack set over a paper towel-lined baking sheet to drain. Repeat with remaining donuts and donut holes. (Donut holes take 60 to 90 seconds and tend to flip themselves.)
In a large bowl, combine sugar, light brown sugar, cinnamon, nutmeg, and salt. One by one, toss the hot donuts in the sugar mixture until well coated. Serve immediately. After the donuts are cool, store in an airtight container for up to 24 hours.