Activate the yeast by combining warm milk and sugar, sprinkle yeast over it, and let sit until foamy.

Prepare the dough by mixing granulated sugar, eggs, softened butter, salt, and vanilla extract in a bowl. Add yeast mixture and gradually add flour until shaggy dough forms.

Knead the dough until smooth and elastic either by hand or with a stand mixer.

Let the dough rise in a greased bowl until doubled in size, about 1 to 1.5 hours.

Roll out the dough and cut into donut shapes, then let rise again until puffy.

Heat oil to 350°F and fry donuts until golden brown on both sides.

Draining on a wire rack, prepare the glaze by whisking together powdered sugar, milk, vanilla extract, and salt.

Dip warm donuts in the glaze and let set before serving.