In a small pot, combine 1/2 cup whole milk and 1/2 cup smooth peanut butter. Heat over low heat, stirring until smooth. Remove from heat and let the mixture cool to lukewarm before using.

In a small bowl, stir 2 teaspoons active dry yeast into 1/4 cup warm water. Let sit about 5 minutes, until foamy.

In the bowl of an electric mixer, whisk together 2-1/2 cups all-purpose flour, 1/2 teaspoon kosher salt, and 1/4 cup sugar.

Add the foamy yeast mixture, the cooled peanut butter–milk mixture, and 1 large beaten egg to the dry ingredients. Mix until combined, then switch to the dough hook.

With the dough hook, knead the dough about 8–10 minutes, until the dough is smooth and pulls away from the sides of the bowl.

Lightly oil a clean bowl, transfer the dough to the bowl, and turn it once to coat with oil. Cover the bowl with oiled plastic wrap and place in a warm area. Let the dough rise 1–2 hours, until doubled in size.

After the first rise, gently deflate the dough and transfer it to a lightly floured surface. Pat or roll the dough to about 1 inch thickness.

Using a large round biscuit cutter (about 3 inches), cut out doughnuts. You should get about 8 doughnuts. Re-shape scraps as needed and cut additional pieces.

Place the cut doughnuts on a parchment- or silpat-lined baking sheet. Cover loosely with oiled plastic wrap and let rest about 1 hour, until they have puffed and nearly doubled in size.

Pour vegetable oil into a wide, heavy pot to a depth of about 3 inches. Heat the oil to 365°F (use a thermometer). Fry the doughnuts in batches without overcrowding the pot. Carefully lower each doughnut into the oil and fry until the underside is golden brown, then flip and fry the other side until golden.

Use a slotted spoon to transfer fried doughnuts to a paper towel–lined plate to drain. Continue frying remaining doughnuts, monitoring the oil temperature so it stays near 365°F and the doughnuts do not burn. Let the doughnuts cool a few minutes until safe to handle.

While the doughnuts cool slightly, stir 3/4 cup seedless blackberry jelly until smooth and transfer it to a squeeze bottle or piping bag.

Using a long wooden skewer, poke a hole into each doughnut from one side toward the center. Insert the squeeze-bottle nozzle into the hole and gently squeeze in jelly, pulling the nozzle back slightly as you fill until a little jelly begins to come out the hole. Repeat on the opposite side if desired.

Sprinkle filled doughnuts with powdered sugar and serve.