In a large mixing bowl, whisk together 1 cup flour, ¼ cup sugar, 2 ¼ tsp (1 packet) instant yeast and ¼ tsp salt.
Add warm milk, 3 Tbsp melted butter, 2 egg yolks and ½ tsp vanilla extract, and whisk vigorously to combine well.
Cover with plastic wrap and rest at room temperature 10 minutes, until some bubbles form on the surface.
Add remaining 1 ½ cups flour, adding just enough until dough holds together and no longer sticks to the sides of the bowl (Add the last 2 Tbsp of flour only if needed) and knead in the bowl 5 minutes. If dough is really sticking to your hands, dust lightly with flour then continue kneading with clean dry hands. Cover the bowl with plastic wrap and let rise in a 100˚F oven for 45 min or at room temperature for 1 ½ hours, or until doubled in size.
Line a baking sheet with parchment paper and preheat oven to 375˚F with rack in the center of the oven.
Turn dough out onto a floured surface and roll the dough out to just under ½” thick. Cut circles using a 2 ½ inch round cookie cutter. Re-roll scraps if needed to make 12 donuts total. Place donuts on prepared baking sheet, cover with a tea towel and let rise in a 100˚F oven for 20 min or at room temperature 45 min, or until puffed. Bake uncovered in the center of a preheated oven at 375˚F for 10-12 minutes or until lightly golden on top.
Right out of the oven, brush a hot bun all over with remaining 1 Tbsp melted butter and roll in a bowl of sugar to coat lightly with sugar. Cut a deep slit in the side of each donut and pipe jam with a pastry bag into each one.
