Make the donut dough according to the relevant recipe instructions.

Place the dough in a lightly greased container with a tight-fitting lid, cover, and place in the refrigerator to chill for about an hour, or up to 2 days.

Turn out the chilled dough onto a lightly floured surface and using a very light touch, sprinkle it very lightly with more flour and knead it lightly by scraping the dough off the floured surface with a floured bench scraper, then folding it over on itself.

Smooth the dough into a rectangle about 1-inch thick, sprinkling very lightly with flour to prevent sticking.

With a floured round cookie cutter about 1 ½-inches in diameter, cut out rounds of dough and place each piece on a parchment-lined baking sheet about ½-inch apart from one another.

Cover the baking sheet with lightly oiled plastic wrap, and set in a warm, draft-free location to rise for 30 minutes, or until puffed but not doubled in volume.

Place about 3-inches of frying oil in a medium-size, heavy-bottom pot or fryer.

Clip a deep-fry/candy thermometer to the side of the pot or fryer, and place the oil over medium-high heat.

Bring the oil temperature to 350°F.

Place the raised donut holes a few at a time in the hot oil, taking care not to crowd the oil.

Fry until very lightly golden brown all over (1 to 2 minutes per side).

Place the confectioners’ sugar and 1 tablespoon of milk in a small bowl and mix well, until a very thick paste forms.

Add more milk by the drop, mixing to combine well, until the glaze falls off the spoon slowly, in a thick but pourable glaze.

Immerse each cooled donut hole in the glaze and lift out with the tines of a fork or chocolate dipping tool, and return to the wire rack for any excess glaze to drip off.

Allow the glaze to set at room temperature and serve immediately.