1. In a large bowl, whisk together 1 cup flour, 1/4 cup sugar, 2 1/4 teaspoons instant yeast, and 1/4 teaspoon salt.
2. Add warm milk, 3 tablespoons melted butter, 2 egg yolks, and 1/2 teaspoon vanilla extract. Whisk until well combined. Cover with plastic wrap and let it sit at room temperature for 10 minutes until some bubbles form on the surface.
3. Add the remaining 1 1/2 cups flour gradually, adding just enough until the dough holds together and doesn’t stick to the sides of the bowl. Knead the dough in the bowl for 5 minutes. If the dough sticks to your hands, sprinkle a little flour and continue kneading until smooth.
4. Cover the bowl with plastic wrap and let it rise in a 100°F oven for 45 minutes or at room temperature for 1 1/2 hours, or until doubled in size.
5. Line a baking tray with parchment paper and preheat the oven to 375°F with a rack in the middle of the oven.
6. Turn the dough out onto a floured surface and roll it out to 1/2 inch thickness. Cut out circles using a 2 1/2-inch round cookie cutter. Re-roll the scraps if needed to make 12 donuts. Place the donuts on the prepared baking tray, cover with a tea towel, and let them rise in a 100°F oven for 20 minutes or at room temperature for 45 minutes, or until puffed.
7. Bake in the middle of the preheated 375°F oven for 10-12 minutes or until slightly golden.
8. Right out of the oven, brush the entire warm donuts with the remaining 1 tablespoon melted butter and roll them in a bowl of sugar to coat evenly. Cut a deep slit in the side of each donut and pipe jam using a pastry bag into each one.
Enjoy your delicious homemade baked donuts!
