Buca di Beppo Little Hat Pasta with Spicy Chicken (Orecchiette Pugliesi)

Source: Chef Vittorio Renda - Buca di Beppo

3/4 cup olive oil
2 tablespoons chopped garlic
2 teaspoons crushed red pepper flakes
2 (6 ounce) boneless, skinless chicken breasts,
   diced into 1-inch square pieces
2 cups broccoli florets, blanched
1 small zucchini, thinly sliced and blanched
1 teaspoon salt
1 pound orecchiette
1 medium tomato, chopped
1/4 cup grated pecorino Romano cheese

In a large saut