Bring 3/4 cup whole milk to a boil in the microwave or over medium heat in a small pot. Watch closely to ensure that the milk doesn't boil over. Pour the milk into a measuring cup and let it cool to between 120 (F) and 130 (F). Sprinkle 3 1/4 teaspoons instant yeast over the surface of the milk, and give the mixture a quick whisk. Set aside for 5 minutes to allow the mixture to get bubbly — this means your yeast is activating! While the yeast is activating, combine 3 1/2 cups all-purpose flour, 1/4 cup granulated sugar, and 1 teaspoon kosher salt in the bowl of a freestanding electric mixer fitted with a paddle attachment. Beat the ingredients on low speed to combine. Add the milk and yeast mixture (make sure it's bubbly before you do), and immediately add 2 large eggs and 2 large egg yolks. Mix on low speed until just combined, and switch out the paddle attachment with the dough hook. With the dough hook, knead the dough on low speed, about 3 minutes. At this point, you could add a bit more flour if necessary, but resist the urge to add too much — I wouldn't add more than 1/2 cup. The dough should be workable but still somewhat sticky.
With the dough hook on low speed, add 6 tablespoons butter, a piece or two at a time. It may look like the butter isn't incorporating, but don't worry — it will! You might have to stop the mixer and knead the butter in with your hands to help incorporate it. Just keep kneading; I promise it'll work. It just takes a while! Once all the butter is incorporated, increase the mixer speed to medium and knead the dough for another few minutes until it turns completely smooth and elastic. You can tell it's done when it looks tacky and is no longer sticky.
Transfer the dough in a slightly greased bowl, cover with plastic wrap, and refrigerate for at least 3 hours, but preferably overnight. During this time, the dough will rise and double in size.
When the dough has chilled, line two baking sheets with parchment paper. Spray the parchment paper generously with cooking spray.
Tip the cold dough onto a lightly floured work surface and roll it into a rough nine by 13-inch rectangle about 1/2-inch thick. Use a 3 1/2-inch cookie cutter to cut out 12 dough rounds and set them on the prepared sheets. Sprinkle a light dusting of flour over the top of each dough round and lightly cover them with plastic wrap. Set in a warm place to proof until the dough is puffy and springs back slowly when pressed gently, about one hour. At this point, it's time to fry the donuts! Line a wire rack with paper towels. Put 1/2 cup granulated sugar and 2 teaspoons sumac in a medium bowl, whisking to combine. Add vegetable oil to a medium, heavy-bottomed pot until you have about two inches of oil. Attach a deep-fry thermometer to the side of the pot and heat the oil to 375 (F). Carefully add 1 to 2 donuts to the oil and fry them until golden brown, around 1 to 2 minutes per side. Use a slotted spoon to fish the donuts out of the oil and transfer them to the prepared wire rack. After about 1 or 2 minutes, when the doughnut are cool enough to handle, toss them in the bowl of granulated sugar until coated. Repeat with the remaining dough. To fill the donuts, use a Bismarck pastry tip (or the handle of a wooden spoon) to poke a hole into one side of each, making sure not to poke through to the other side. Fill a pastry bag with a small round tip (or a Bismarck pastry tip) with the jam of your choice. Insert the tip of the pastry bag into the hole and gently squeeze to fill each doughnut. The donuts are the best on the day they're made.