Heat 1 tablespoon extra virgin olive oil in a wide pot over medium heat. Add the onion and fennel and sauté for 5 to 6 minutes until they soften. Add the garlic and sauté for 1 minute until fragrant. Season lightly with salt and pepper.
Add the Roma tomatoes and chickpeas. Season with salt, pepper, and ¼ teaspoon crushed red pepper. Add the water and bring to a boil. Reduce the heat to low and simmer, uncovered, for 20 to 30 minutes.
Mash some of the chickpeas during cooking to create a thicker sauce. Add another splash or two of water if the sauce reduces too much. Taste and season with salt, pepper, and additional crushed red pepper if desired.
Cook the pasta:
Bring a large pot of generously salted water to a boil. Add the rigatoni and cook according to the package directions until al dente. Scoop out ¼ cup of the pasta cooking water and then drain the pasta.
Finish the pasta:
Turn on the broiler.
Add the cooked pasta to the sauce and toss to coat, adding the reserved pasta water if needed. Continue tossing until the pasta is coated.
Scatter the shredded mozzarella cheese over the pasta and drizzle with a few teaspoons of extra virgin olive oil. Place the pot under the broiler for 2 to 3 minutes or until the cheese is bubbly and browned. Remove from the broiler.
To serve:
Finish the pasta with a few fennel fronds and serve immediately. Enjoy!