1 tablespoon plus 1 tsp kosher salt
1 pound orecchiette pasta
1 bunch broccolini (about 12 ounces), cut into 1-inch pieces
3 tbsp extra-virgin olive oil
1 1/4 pounds ground lamb
4 garlic cloves, minced
1/4 to 1/2 teaspoon dried red pepper flakes
3/4 cup grated Pecorino Romano or Parmigiano-Reggiano cheese
Bring about 6 quarts of water to a boil in a large pot and season it with 1 tablespoon of salt. Add the pasta and cook until almost tender but still a little underdone, stirring occasionally, about 7 minutes. Add the broccolini to the pot and cook 3 minute more, until the pasta is al dente and the broccolini is bright green and crisp-tender. Drain, reserving about 1/2 cup of the cooking water.
Meanwhile, heat the olive oil over medium-high heat in a Dutch oven or other large pot. Add the lamb and break it up into small chunks. cook, stirring occasionally, until the lamb is deeply browned and a little crispy, about 10 minutes. Stir in the garlic and the pepper flakes (to taste), season with 1 teaspoon of salt, and cook about 1 minute longer.
Reduce the heat to medium-low and stir the pasta and broccolini into the pot with the lamb. Add the reserved cooking water and continue cooking about 1 to 2 minutes more, to allow the pasta to absorb the flavors. Sprinkle in about 1/2 cup of the cheese and stir to combine well. Serve the pasta in warm bowls with the remaining 1/4 cup of cheese sprinkled over the top.