Bring 6 quarts of water to boil in a pasta pot with 1 ½ TBSP of Salt. Cook orrechiette according to directions until al dente, 12-15 minutes.
In a large saute pan, brown the sausage in 1 TBSP oil over medium-high heat, breaking it up as it cooks. If very lean, you may need to add another TBSP of oil. Remove from the pan.
In the same pan, add 1-2 TBSP oil (depending on how much remained from sausage), reduce heat to medium and add the red pepper flakes and garlic and give a quick stir, being sure not to let the garlic brown. Add the broccolini and stir fry to coat in the oil.
Increase heat to medium high and add the wine, give a quick stir to deglaze, scraping up the bits and cover. Allow to steam for 1 minute and remove from heat. It should be bright green but still crunchy.
Return sausage to the pan. When the pasta is ready, bring heat to medium.
Drain the pasta and add to the sausage and broccolini, along with 1-2 TBSP pasta water. Add the cheese , ¼ tsp black pepper and stir together until well blended and the cheese has melted.
Serve immediately with a fresh grating of cheese and drizzle of olive oil.