Make Lemon Curd:

1. Cook Curd: Set a medium saucepan with water to simmer. In a small heatproof bowl, whisk together the lemon juice, zest, sugar, and eggs until well combined. Add the butter pieces and set the bowl over the simmering pot of water. Whisk the mixture continuously while cooking until it’s thick, about 10 minutes.
2. Strain and Chill: Remove from heat and pass the curd through a fine-mesh sieve. Cover the curd with plastic wrap, directly on the curd, and let cool. Chill for a few hours or overnight.

Make Donuts:

1. Activate Yeast: In a small bowl, combine the yeast and warm water. Mix until yeast dissolves and let stand for 5-10 minutes until foamy. (If yeast is not foamy, do not continue. Start again with new yeast.)
2. Make Dough: In the bowl of an electric mixer fitted with the hook attachment, mix the flour, milk, butter, egg yolks, sugar, salt, cinnamon, nutmeg, and yeast mixture on low speed until dough comes together. Knead dough for 3-5 minutes until elastic and smooth. (Alternatively, mix the ingredients in a medium bowl with a wooden spatula until the dough comes together. Turn dough onto a well-floured surface and knead for 7 minutes until the dough is smooth and elastic.)
3. First Rise: Transfer dough into a lightly oiled large bowl and sprinkle lightly with flour. Cover the bowl loosely with a kitchen towel and let rise until double in size, about 2 hours in a draft-free place at room temperature. (Alternatively, you can let the dough rise in the refrigerator for 8-12 hours or overnight).
4. Shape Donuts: Lightly flour a surface and turn out the dough. Roll dough out to about half-inch thick. Using a biscuit cutter or round cookie cutter, cut out as many rounds as possible. Transfer the donuts to a lightly floured baking sheet. Cover the baking sheet loosely with a kitchen towel and let donuts rise at room temperature until slightly puffed, about 30-45 minutes.
5. Fry Donuts: When ready to fry, heat the vegetable oil in a deep heavy-bottomed pot over medium-high heat. The oil should be at least 2 ½ inches deep. If you like, you can check the oil with a thermometer; it should be about 350 degrees F. Fry donuts, 3-4 at a time, until puffed and golden brown, about 1-2 minutes. Make sure you turn the donuts occasionally as they fry. Remove from oil with a slotted spoon and transfer to a paper towel-lined plate.
6. Fill and Serve: Let donuts cool completely. To fill donuts, use a long-tipped pastry bag to poke a hole in each donut and fill with lemon curd. Roll donuts generously in granulated sugar or powdered sugar. Enjoy!