1. Prepare the Dough

1. In a small bowl, mix the warm milk and yeast. Let sit for 5-10 minutes until foamy.
2. In a large mixing bowl, combine the flour, sugar, and salt.
3. Add the eggs, softened butter, vanilla extract, and the activated yeast mixture. Mix until a dough forms.
4. Knead the dough on a lightly floured surface for about 8-10 minutes, until smooth and elastic.
5. Place the dough in a greased bowl, cover with a clean towel, and let it rise in a warm place for about 1 ½ hours, or until doubled in size.

2. Shape the Doughnuts

1. Roll the dough out on a floured surface to about ½-inch thickness.
2. Cut into strips (about 6 inches long and 1 inch wide). Twist each strip and pinch the ends to hold the shape.
3. Place the twisted dough on a parchment-lined baking sheet, cover, and let rise for another 30 minutes.

3. Fry the Doughnuts

1. Heat oil in a deep fryer or large pot to 350°F (175°C).
2. Fry the doughnuts in batches for 1-2 minutes per side, or until golden brown.
3. Remove with a slotted spoon and drain on a paper towel-lined plate.

4. Coat with Cinnamon Sugar

1. Mix the granulated sugar and cinnamon in a shallow dish.
2. While the doughnuts are still warm, toss them in the cinnamon sugar mixture to coat evenly.