Penne with sausage, fennel and pecorino

Kosher salt, 4 Tbs. extra-virgin olive oil, 12 oz. sweet Italian sausage, casings removed, 2 medium yellow onions, halved and thinly sliced (about 3 cups), 1 large fennel bulb (about 1-1/2 lb.), halved, cored, and thinly sliced crosswise (about 4 cups), 2 Tbs. chopped fresh sage, 1 cup lower-salt chicken broth, 10 oz. dried penne, 1 oz. finely grated Pecorino Romano (1 cup using a rasp grater); more for serving, Freshly ground black pepper

Bring a large pot of well-salted water to a boil over high heat. Meanwhile, heat 2 Tbs. of the oil in a heavy-duty 12-inch skillet over medium-high heat. Add the sausage and cook, stirring and breaking it up into smaller pieces with the edge of a slotted metal spoon, until browned and cooked through, about 5 minutes. Use the spoon to transfer the sausage to a paper-towel lined plate and pour off any fat left in the skillet.
Set the skillet over medium-high heat and add the remaining 2 Tbs. oil and the onion.Cook, stirring occasionally, until it softens and begins to brown, about 10 minutes. Stir in the fennel, sage, and 1/4 tsp. salt. Lower the heat to medium and cook, stirring occasionally, until the fennel is softened and the onion is golden, about 5 minutes. Add the cooked sausage and chicken broth and cook, stirring, until heated through, about 2 minutes.
Meanwhile, cook the penne in the boiling water, stirring occasionally, until cooked through, 10 to 11 minutes. Reserve 1 cup of the pasta water and drain the pasta in a colander. Return the pasta to the pot over medium-high heat and stir in the sausage mixture until well combined. Remove from the heat and stir in the cheese, 1/4 tsp. pepper, and enough reserved pasta water to moisten, if necessary. Distribute among 4 bowls and sprinkle with additional cheese.