Add the flour, sourdough starter, lukewarm milk, eggs, butter, sugar, and salt to the bowl of your stand mixer.

Fit the mixer with the dough hook. Mix on low until all the ingredients are combined, then on medium-low for 5 to 8 minutes, until the dough is smooth and slightly tacky. The dough should feel soft and slightly tacky, but not wet or sticky. If it feels too dry, add water 1 tablespoon at a time. If it is too wet, add flour 1 tablespoon at a time.

Cover the bowl and let it rise at room temperature for 6 to 12 hours, or until it has nearly doubled in size and looks puffy. An overnight rise works well.

Turn the risen dough onto a lightly floured surface.

Cut the dough into 12 pieces at that weight. For evenly sized donuts, weigh the dough and divide the total weight by 12.

Place one piece of dough in your palm. Fold the edges toward the bottom to create a smooth surface. Set it on the counter, seam side down.

To use the cupping method, place your hand over the dough with your fingers gently curved around it. Move your hand in small circles against the counter while keeping the dough underneath your palm. The friction will tighten the surface and create a smooth, round ball.

Repeat this with the remaining dough.

Line a baking sheet with parchment paper and lightly dust it with flour. Place the dough balls on the parchment, leaving space between them. Cover them loosely with plastic wrap or a towel and let them rise for 1½ to 3 hours, or until they become puffy and light.

Heat 1 to 2 quarts of neutral oil in a large, heavy-bottomed pot to 350°F.

Gently place 2 to 3 donuts into the hot oil per batch, frying for 1½ to 2 minutes on each side and turning once, until it turns deep golden brown. Move them onto a paper-towel-lined baking sheet or to a wire rack and repeat with the remaining donuts. Let the oil return to 350°F between batches.

Let the donuts cool for 5 to 10 minutes, until they are warm but not hot. While they are still warm, roll them in the granulated sugar, coating all sides.

Transfer the grape jelly to a piping bag. (Tip: Place the bag in a tall glass, fold the top edges over the rim, and spoon in the jelly.)

Poke a hole into the side of each donut using a chopstick, inserting it about ¾ of the way in and gently rotating it to create an internal pocket.

Insert the tip of the piping bag into the hole and gently squeeze it while slowly pulling the tip out, until the donut feels heavy and filled, with a small amount of jelly visible at the opening.

Serve immediately and enjoy!