Combine dry ingredients: flour, sugar, yeast, and salt in a large mixing bowl.
In a separate bowl, whisk together warm milk, egg, melted butter, and vanilla extract. Pour into dry ingredients and stir until a dough forms.
Knead the dough on a floured surface for 5-7 minutes until smooth and elastic. Place in a greased bowl, cover, and let rise for 1 hour.
Preheat oven to 350°F. Punch down the dough, roll out to 1/2 inch thick, and cut out donut shapes.
Place cut donuts on a parchment-lined baking sheet, cover, and let rise for 30 minutes.
Bake donuts for 12-15 minutes until golden brown.
Cool slightly, make an indentation in each donut, and fill with jam. Dust with powdered sugar before serving.