Pre-heat the oven to 400°F.
Bring large pot of water to a boil, salt it, add the broccoli rabe and cook for 8 minutes; drain.
In a large skillet, heat about 1/4 cup EVOO, four turns of the pan, over medium heat. Add the chili pepper and garlic and swirl for 1-2 minutes. Add the broccoli rabe and toss for 2-3 minutes. Turn off the heat.
In a medium size bowl, combine the ricotta, Pecorino, Parmigiano, thyme and the remaining 2 tablespoons EVOO; season with salt and pepper. Place the bread on a baking sheet and slather both halves evenly with the ricotta mixture. Top with the broccoli rabe and mozzarella (or provolone). Bake until melted and bubbly, about 10 minutes. Cut into large chunks to serve.