1. Heat oil in a large braising pan or skillet with a cover. Add onion; sauté over medium heat until softened, about 5 minutes. Stir in fennel; sauté until golden, about 10 minutes. Add 1/2 cup water and season to taste with salt and pepper. Cover and simmer over medium-low heat until fennel is tender, about 8 minutes longer. Stir in vinegar; simmer to blend flavors, 1 minute longer. Adjust seasonings. 2. Meanwhile, bring 4 quarts water to boil in large pot. Add 1 tablespoon salt and the pasta; return to boil. Add kale; continue to cook until pasta is al dente, about 7 minutes. 3. Drain pasta and greens; toss with fennel mixture and cheese. Transfer portions to warm pasta bowls. Garnish with reserved minced fennel fronds. Serve immediately with more cheese passed separately.