In a small bowl, combine warm milk, yeast, and sugar. Let stand for 5 minutes, or until foamy.

In a large bowl, whisk together the egg, melted butter, and vanilla extract.

Add the yeast mixture to the egg mixture and stir to combine.

In a separate bowl, whisk together the flour and salt. Gradually add the dry ingredients to the wet ingredients, mixing until a dough forms.

Turn the dough out onto a lightly floured surface and knead for 5-7 minutes, or until smooth and elastic.

Place the dough in a greased bowl, cover with plastic wrap, and let rise in a warm place for 1 hour, or until doubled in size.

Punch down the dough and divide it into 12 equal pieces. Roll each piece into a long, thin rope.

Twist the rope into a cruller shape and place it on an ungreased baking sheet. Repeat with the remaining dough.

Let the donuts rise for 30 minutes, or until doubled in size.

Preheat oven to 375?F (190?C).

Bake the donuts for 15-20 minutes, or until golden brown.

Let the donuts cool on a wire rack for a few minutes.

In a small bowl, whisk together the powdered sugar, milk, and vanilla extract until smooth.

Dip the cooled donuts into the glaze and let them set before serving.