In a small bowl, combine the warm water, yeast, and 1 teaspoon of granulated sugar. Stir and let sit for 5–10 minutes until foamy and frothy—this means the yeast is active.
2. Make the Dough:
In a large mixing bowl, stir together the remaining sugar, salt, flour, butter, warm milk, and egg.
Add the activated yeast mixture and stir until a soft dough begins to form. It should be slightly sticky but manageable.
3. Knead and Rise:
Transfer the dough to a floured surface and knead for 5–7 minutes until smooth and elastic. Add a small amount of flour as needed to keep from sticking, but avoid over-flouring.
Place the kneaded dough in a lightly oiled bowl. Cover with plastic wrap or a clean towel and let rise in a warm area for about 1 hour, or until doubled in size.
4. Shape the Donuts:
Punch down the risen dough and roll it out to about 1/2-inch thickness on a floured surface.
Use a donut cutter or two round cutters (one large, one small) to cut out donuts and holes. Re-roll scraps as needed.
Place the cut donuts and holes onto a floured baking sheet, cover, and let rise again for 30–40 minutes until puffy.