How to Make It
Preheat broiler with oven rack 8 inches from heat. Heat a cast-iron griddle over two burners on stovetop over medium; brush with oil. Place 2 tortillas in a single layer on hot griddle. Spread 2 tablespoons marinara sauce on each tortilla. Scatter 1/2 cup pepper Jack cheese over marinara on each; top with remaining 2 tortillas. Cook until crisp and lightly browned on bottoms, about 3 minutes. Flip quesadizzas. Spread remaining 2 tablespoons marinara sauce evenly over quesadizzas, and sprinkle evenly with remaining 1/2 cup pepper Jack cheese. Arrange linguiça slices evenly over quesadizzas.
Transfer quesadizzas to a rimmed baking sheet. Broil in preheated oven until cheese is melted and linguiça is slightly curled, 1 to 2 minutes.
Slice quesadizzas into wedges. Serve with Parmesan, oregano, and crushed red pepper.