Rigatoni with Broccoli and Sausage

Name: Rigatoni with Broccoli and Sausage
Ingredients: 3 to 4 garlic cloves, very thinly sliced; Extra-virgin olive oil; 1 pound sweet or hot Italian sausage, bulk or casings removed; Kosher salt and freshly ground black pepper; 8 ounces rigatoni; 1 pound broccoli, stems trimmed and peeled, stems sliced crosswise into 1/4-inch coins, and tops cut into florets; 1/4 teaspoon dried chile flakes; 1/2 cup Whipped Ricotta (see recipe below); About 1 cup freshly grated Parmigiano-Reggiano; 1/4 cup dried breadcrumbs (optional); 1 1/2 cups whole-milk ricotta cheese; 1/2 teaspoon kosher salt; Freshly ground black pepper; 1/4 cup extra-virgin olive oil, plus more as needed