How to Make It
Prepare hot roll mix with hot water, butter, and egg according to package directions, through letting dough rest 5 minutes (step 4 according to Pillsbury package directions).
Place dough ball in a greased bowl, and cover with plastic wrap. Let rise in a warm place (80°F to 85°F) until dough has doubled in size, about 30 minutes.
Pour oil to a depth of 2 inches in a medium Dutch oven, and heat over medium to 350°F. Stir together sugar, cinnamon, and salt in a medium bowl; set aside.
Turn dough out onto a well floured surface, and roll into a 15-inch-wide circle. Using a 3-inch cutter, cut 16 circles from dough. Cover 3-inch circles with a damp towel to keep from drying out.
Working about 4 at a time, place dough circles in hot oil, and fry until golden and puffed, about 1 minute and 30 seconds to 2 minutes per side. Using a slotted spoon, transfer to a wire rack over a few layers of paper towels. Dip doughnuts in sugar mixture, and return to rack.
Spoon jelly into a ziplock plastic freezer bag, and snip a small hole in corner of bag. Using a paring knife, cut a small slit into side or top of each doughnut. Pipe jelly evenly into doughnuts. Serve immediately or at room temperature.