3 1/2 cups flour, plus 1 cup for rolling and cutting
1 1/2 teaspoons kosher salt
1 teaspoon baking soda
1/2 teaspoon baking powder
1/4 teaspoon baharat (spice blend; see headnote)
Canola or peanut oil, for frying
For the tahini glaze
3 3/4 cups confectioners’ sugar
1/2 cup tahini (see headnote)
1/2 cup water
1 tablespoon kosher salt
1/2 cup roasted/toasted sesame seeds
For the dough: Combine the egg yolks and sugar in the bowl of a stand mixer or use a handheld electric mixer; beat on low speed for about 3 minutes, until ribbons start to form in the mixture and the color lightens. Over the next 30 seconds, gradually add the melted/cooled butter in a steady stream.
Add all the buttermilk at once, beating for about 5 seconds until just incorporated.
Whisk together the 3 1/2 cups of flour, the salt, baking soda, baking powder and baharat in a mixing bowl, then add to the buttermilk mixture all at once. Beat on low speed for about 30 seconds, until incorporated. Stop to scrape down the sides of the bowl. Beat on medium-low speed for 20 to 30 seconds, until the dough looks smooth and starts to pull away from sides of the bowl.
Prepare a counter work space by fastening a large piece of parchment paper with tape at the corners. Have the 1 cup of flour nearby to use as needed; use about 1/2 cup of it to flour the parchment paper.
Scrape down the paddle attachment and turn all the dough out onto the floured paper. Dust the top of the dough with some of the remaining 1/2 cup of flour, sprinkling the edges as well. Flour your hands and a rolling pin — although you may not need the latter, because the dough is soft.
Pat or roll out the dough into a 1/2-inch-thick rectangle, about 10 by 14 1/2 inches. Add more flour to prevent sticking, but remember to use a pastry brush to get clear away any excess flour on the dough and parchment. Unfasten the parchment from the counter, then slide it and the dough onto the back of a baking sheet. Freeze for up to 30 minutes so that the dough firms up.
Flour the cutters. Cut a total of 14 to 18 doughnuts and as many doughnut holes as you can, rerolling the scraps as needed.
Return the baking sheet with the shaped doughnuts to the freezer until ready to fry.
(At this point, the frozen rings can be wrapped in plastic and stored in the freezer for up to 2 days. Let defrost slightly before frying.)
When you’re ready to fry the doughnuts, heat 2 or 3 inches’ worth of the oil in a wide, heavy pot (preferably enameled cast-iron) over medium to medium-low heat, until the oil temperature reaches 375 degrees. Line a rimmed baking sheet with paper towels, then seat a wire rack over it.
Use a spatula to transfer 4 of the dough rings to the oil. After about 90 seconds, the undersides will begin to brown; flip the doughnuts with a slotted spoon. Fry for another 60 to 90 seconds until golden brown and delightfully puffy. (Doughnut holes take 60 to 90 seconds and tend to flip themselves.) Use a slotted spoon to transfer the doughnuts to the wire rack to drain. Make sure the oil returns to 375 degrees before frying each subsequent batch.
While the doughnuts cool for 20 minutes, make the glaze: Whisk together the confectioners’ sugar, tahini, water, salt and sesame seeds in a mixing bowl, until smooth.
Dunk the doughnuts and holes in the glaze and return to the wire rack to set before serving.