Preheat oven to 375 degrees F (190 degrees C). Grease a 12-cup muffin tin with butter or cooking spray.
In a small bowl, dissolve yeast in warm milk. Let stand for 5 minutes.
In a large bowl, combine flour, sugar, and salt. Stir in melted butter, egg, vanilla extract, and yeast mixture until well blended.
Knead dough until it is smooth. Divide dough into fourths. On a lightly floured surface, roll out each piece of dough into a 12-inch-long rope. Make a U-shape with the ropes and press the ends together to form a donut shape.
Fill the center of each donut with the desired filling. If desired, brush with egg white and sprinkle with cinnamon sugar. Bake in the oven for 30 to 35 minutes, or until golden brown.