Proof the dough: scrape your mixing bowl clean, lightly oil the inside and place the dough seam-down into the bowl. Cover it with a kitchen towel or plastic wrap and let rise in a warm, draft-free spot for about 60 minutes or until roughly 1½ times larger in volume.
Divide the dough: remove the proofed dough from the bowl and onto a lightly floured surface. Gently press it into a rectangle. With the long edge facing you, use a bench scraper or knife to divide the dough horizontally into three rows, then divide each row into four, creating 12 equal pieces.
Shape the doughnuts: generously oil a clean sheet pan (or two if they're small) and set aside. Keeping the other pieces covered with plastic so they don't dry out, roll one piece at a time into a very tight ball, making sure the seam at the bottom is completely sealed. Repeat for the other pieces, then set them on the oiled sheet pan(s) at least 2" apart from each other.
The dough can become very difficult to seal if it starts to dry out. To remedy this, have a small cup of cold water nearby and sprinkle a little bit over your work surface as needed. You should immediately feel the dough start to stick to the table as you roll, making it easier to tighten and seal. (If the dough just slides around in the water, you've added too much; mop up the excess with a towel and keep going!)
Proof the doughnuts: cover the sheet pan(s) loosely with a plastic bag and let rise for about 1½ - 2 hours in a warm, draft-free spot until each is about 2½ - 3" in diameter.