In a large mixing bowl, whisk together 1 cup flour, 1/4 cup sugar,
2 1/4 tsp (1 packet) instant yeast and 1/4 tsp salt.
Add warm milk, 3 Tbsp melted butter, 2 egg yolks and 1/2 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 1/2 cups flour, adding just enough until dough
holds together and no longer sticks to the sides of the bowl.
Knead in the bowl for 5 minutes. If dough is really sticking to
your hands, dust lightly with flour then continue kneading with
clean dry hands.
Cover bowl with plastic wrap and let rise in a 100°F oven for
45 min or at room temperature for 1 1/2 hours, or until doubled
in size.
Line a baking sheet with parchment paper and preheat the oven to
375°F with a rack in the center of the oven.
Turn dough out onto a floured surface and roll the dough out to
just under 1/2" thick. Cut circles using a 2 1/2 inch round
cookie cutter. Re-roll scraps if needed to make 12 donuts total.
Place donuts on a 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.