Whisk warm milk, yeast, and sugar in a large bowl and let sit 5 minutes until foamy.
Add flour, eggs, and salt; mix with dough hook on low speed for 1 minute.
Scrape bowl sides and mix at medium speed for 2 minutes.
Add butter one tablespoon at a time, mixing until dough is smooth and elastic.
Transfer dough to greased bowl, cover, and let rise in warm place until doubled, about 60 to 90 minutes.
Punch down dough, transfer to floured surface, shape into ball, and cut into 16 pieces.
Roll each piece into tight balls and place on baking sheets to rise until nearly doubled, about 30 minutes.
Heat oil in a dutch oven or deep fryer to 330°F to 350°F.
Fry donuts until golden brown, about 2 minutes per side.
Drain and toss donuts in granulated sugar.
Fill each donut with jam using a piping bag.
Serve donuts warm for best flavor and texture.