Heat oven to 375° F. Heat the oil in a large skillet over medium-high heat. Add the broccoli rabe, garlic, ½ teaspoon salt, and ¼ teaspoon pepper. Cook, tossing frequently, until the broccoli rabe is tender, 4 to 5 minutes. Transfer to a plate and let cool.
On a lightly floured work surface, roll the pastry into a 10-by-15-inch rectangle. Leaving a 1-inch border, prick holes in the pastry with a fork. Top with the mozzarella, broccoli rabe, and pecorino. Bake on a parchment-lined baking sheet until the pastry is golden brown, 25 to 30 minutes. Cut into squares.