Preheat the oven to 375 degrees F. Line 1 baking sheet with foil and another with parchment.
Toss the sausages with 1 tablespoon of the oil on the foil-lined baking sheet, and bake, flipping the sausages halfway through, until lightly browned and fully cooked, about 30 minutes. Let cool.
Lower the oven temperature to 350 degrees F. Toss together the provolone and mozzarella in a medium bowl. Make a slit down the length of each sausage, cutting about halfway through, and fill each with 1 teaspoon pesto, 2 pepper strips and 1 scant tablespoon of the cheese mixture; reserve any remaining cheese mixture.
Open the tube of dough, find the seam and carefully unroll the dough on a lightly floured surface. Cut 6 strips 1 1/4 inches by 12 inches. Wrap 1 strip around a stuffed sausage link, coiling the strip from 1 end of the link to the other, leaving a 1/4-inch space between dough turns and leaving the ends of the sausage slightly exposed. Repeat with the remaining dough strips and sausages, setting the finished rolls at least 1 inch apart on the parchment-lined baking sheet.
Brush the rolls with the remaining tablespoon of oil. Sprinkle the tops with the reserved cheese mixture. Bake until golden brown, 20 to 25 minutes. Let cool for a few minutes before cutting each roll into 4 pieces with a serrated knife. Serve warm with warm pizza sauce on the side.