Heat a large skillet over medium-high heat. Cook and stir chorizo in the hot skillet until browned and crumbly, 5 to 7 minutes. Remove chorizo with a slotted spoon to a plate lined with paper towel to drain, retaining drippings in the skillet.
Saute red bell pepper, red onion, and jalapeno pepper in reserved chorizo drippings until tender, 5 to 7 minutes. Remove with a slotted spoon to a plate lined with paper towel to drain.
Flatten biscuit roll dough into 4 4x6-inch rectangles, pressing seams together where needed. Mix chorizo and vegetable mixture in a bowl; spoon into the center of each rectangle and top with cheese. Roll dough, taking care to seal contents inside the dough. Arrange 'blankets' on a baking sheet so the seams are down. Check for holes and seal as found.
Bake in preheated oven until golden brown, 10 to 12 minutes; transfer to a serving platter and season with hot sauce.