Heat oven to 425° F. Oil a large rimmed baking sheet.
Heat the oil in a large skillet over medium-high heat. Cook the sausages, turning occasionally, until browned and cooked through, 10 to 12 minutes. Slice.
Shape the dough into four 8-inch rounds. Dividing evenly, top half of each round with the sausages, cheese, and broccoli. Fold the dough over and pinch the edges to seal. Place on the prepared baking sheet and brush with oil. Bake until golden brown, 25 to 30 minutes. Serve with the marinara sauce.