Bring a large pot of salted water to a boil and cook the orecchiette pasta until al dente, but be sure to reserve ¾ cup of the pasta water to help make the sauce.
While the pasta is cooking, heat up a tablespoon of olive oil in a large sauté or frying pan large enough to hold the pasta and sauce. When the oil is hot, add the sausage in 1 inch pieces and cook until browned on all sides and cooked through. This should take about 8 minutes. Transfer the sausage to the plate lined with paper towel.
Add another 2 tablespoons of the olive oil to the pan, raise the heat to medium high and as soon as it gets hot, add the tomatoes and crushed red pepper.
While the tomatoes are cooking, use the back of a slotted spoon to press down on them until they are slightly softened. This should take about 5 minutes.
Now add the reserved pasta water, scrape up any brown bits of sausage and cook over medium heat until the liquid is reduced by half. Keep using the back of a slotted spoon to crush the tomatoes. This should all take about 6 minutes.
Add the pasta back to the pan along with the reserved sausage and the remaining tablespoon of extra virgin olive oil. Mix this all-together using your slotted spoon until the pasta is coated with sauce and olive oil.
Remove the pan from the heat, stir in the cheese and serve right away in warm pasta bowls along with any side dishes.