1. In a pot of salted water, blanch the unpeeled garlic cloves for 5 minutes. Drain and dry with paper towels. On very low heat, confit the garlic in olive oil with the dried chili pepper for 10 minutes.
2. Rinse the broccoli. Separate into small florets. Cook in a pot of salted water for 4 minutes. Drain and set aside.
3. In a large pot of salted water, cook the conchiglies according to the package instructions.
4. In the pan with olive oil and garlic, add the broccoli and cherry tomatoes. Sauté over high heat for 2 minutes. Season with pepper.
5. Drain the pasta and transfer it to a large bowl. Add the olive oil, garlic, broccoli, and cherry tomatoes. Serve immediately with grated parmesan.