In the bowl of a stand mixer, combine the warm milk, sugar, and yeast. Briefly whisk to mix, then set aside for 8-10 minutes to activate the yeast.
Add the egg, egg yolk, melted butter, and lemon zest into the bowl. Whisk to combine.
Add the flour. Using the hook attachment, knead on LOW speed for 2 minutes.
Increase the speed to Medium-High to knead 4-6 more minutes. The dough should be smooth and pliable. (If too dry, add more milk. If too wet, add more water.)
Place the dough in a lightly greased bowl. Cover with plastic wrap. Set aside to rise in a warm environment (like oven with light on) for 1-2 hours, until doubled in size.
In the meantime, cutout 4×4” squares of parchment paper. Place them in a single layer on 1-2 baking pans.
Roll out the dough on a lightly floured surface to ½” thick. Using a 2 ½ – 3” cookie cutter, cut the doughnuts. Re-roll the dough as needed to use it all.
Place each doughnut on a single square of parchment paper
Cover the doughnuts with plastic wrap. Set aside to rise 1-2 hours, until doubled in size.
Heat the neutral oil in a large pot over medium high heat to 350F. Using a large spoon or wooden spatula, gently scoop underneath the parchment paper-lined doughnuts to place in the hot oil. Use tongs to remove the parchment paper.
Fry 1-2 minutes on each side, until golden brown.
Using a slotted spoon, remove the doughnuts to place on a paper towel lined plate.
While still warm, toss the doughnuts in more granulated cane sugar
Let cool 10 minutes before adding filling.