Heat milk in a small pot until it’s warm to the touch but not hot (just slightly warmer than room temperature).

In a large bowl, combine flour, sugar, salt, egg, milk, and sourdough starter. Stir with a wooden spoon until the dough comes together. It should feel soft and slightly tacky but not sticky.

Turn the dough onto a floured surface and knead for about 3–5 minutes, just until smooth and elastic. Don’t overwork it. A gentle knead is all it needs.

Divide the dough into 24 even pieces (or 12 for donuts). Roll each piece into a ball for donut holes, or shape into ropes and pinch the ends together for traditional donuts. Place on a parchment-lined baking sheet with a little space between each.

Cover and place in a warm spot to rise for about 1 hour, or until slightly puffy. If your kitchen is cool, you can warm the oven briefly (then turn it off) and set the tray inside with a small bowl of hot water to create steam.

In a small bowl, mix sugar and cinnamon for rolling. Set aside.

Pour oil into a deep fryer or heavy-bottomed pot to a depth of about 2 inches. Heat to 330°F. Keep a close eye on the temperature . Too hot and the donuts will brown too fast; too cool and they’ll soak up oil.

Carefully lower 4–6 donut holes into the oil at a time. They’ll sink at first, then float as they cook. Fry for about 2–3 minutes per side, turning with a slotted spoon once the bottoms turn golden brown.

Remove from oil, drain briefly on paper towels, and while still warm, roll in the cinnamon sugar mixture until evenly coated.