In a small bowl, combine lukewarm milk, sugar, and active dry yeast. Stir gently and let it sit for about 5-10 minutes, or until it becomes frothy.

In a larger mixing bowl, combine melted unsalted butter, egg, and vanilla extract with the yeast mixture. Whisk until smoothly combined.

Sift together the all-purpose flour and salt in a separate bowl. Gradually add this dry mixture to the wet ingredients, stirring gently until a soft dough forms.

Transfer the dough to a lightly floured surface and knead for about 5-7 minutes until smooth and elastic.

Place the kneaded dough in a lightly oiled bowl, cover with a towel, and let it rise in a warm place for 1 to 1.5 hours or until doubled in size.

Punch the risen dough down gently, roll it out to about ½ inch thick, and cut out donut holes. Place them on a floured baking sheet.

Cover the baking sheet with a towel and let the donut holes rise for another 30-45 minutes until puffy.

Heat vegetable oil in a deep pot or fryer to 350°F. Ensure the oil reaches the right temperature for frying.

Fry the donut holes in batches for 1-2 minutes on each side until golden brown, then place on paper towels to drain excess oil.

Melt semi-sweet chocolate and unsalted butter in a double boiler until smooth. Stir in milk, vanilla extract, and a pinch of salt.

Dip each warm donut hole into the chocolate glaze, allowing excess to drip off before placing on a cooling rack.

Let the glazed donut holes sit on the rack for 15-20 minutes to set the glaze properly.