In a bowl, dissolve yeast in warm water and let sit for 5 minutes until foamy.
Add sugar, milk, butter, egg, and vanilla extract, and mix well.
Gradually add flour and salt, kneading until a soft dough forms.
Let dough rise for 1 hour in a warm place until doubled in size.
Roll out dough and cut into donut shapes. Let rest for 15 minutes.
Heat oil in a deep fryer to 350°F (175°C).
Fry donuts for 1-2 minutes per side until golden brown.
Remove and drain on a paper towel. Dust with powdered sugar and serve.