Combine the drained chickpeas, bay leaves, and 2 quarts water. Bring to a simmer, and cook until tender, about 1 hour. Drain, and discard the bay leaves.
Preheat the oven to 350 degrees F. Bring a large pot of salted water to a boil for pasta.
In a large skillet, heat the olive oil over medium-high heat. Add the garlic. Once the garlic is sizzling, add the red-pepper flakes and tomatoes, along with 1 cup of slosh water from the tomato can. Add the sage, salt, and cooked chickpeas. Bring to a simmer, and cook until thickened, about 10 minutes.
While the sauce simmers, cook the pasta until it is al dente. Transfer the pasta with a spider to the sauce, and add 1 cup pasta water. Simmer until the sauce just comes together again, about 1 minute.
Remove the skillet from the heat, and stir in 1 cup grated Grana Padano or Parmigiano-Reggiano.
Grease a 4-quart baking dish with butter, and pour in the pasta and sauce mixture.
In a small bowl, toss together the remaining Grana Padano or Parmigiano-Reggiano and the shredded mozzarella, and sprinkle over the pasta.
Bake until the cheese is bubbly and golden, about 30 minutes. Serve.