Bring a large pot of well-salted water to a boil.
Heat 1-1/2 Tbs. of the oil in a 10-inch straight-sided saute pan over medium-high heat until shimmering hot. Add the sausage and cook, breaking it up with a metal spoon, until browned and cooked through, about 5 minutes. Transfer the sausage to a paper-towel-lined plate and pour off and discard any fat left in the pan.
Set the pan over medium heat and add the remaining 1-1/2 Tbs. oil, the fennel, and 1 tsp. salt. Cook, stirring, until the fennel softens and browns lightly, about 6 minutes. Raise the heat to high, add the wine, and cook, scraping the bottom of the pan to loosen any browned bits, until almost evaporated, 1 to 2 minutes.
Add the sausage, tomatoes, half of the basil, the red pepper flakes, and 1/2 tsp. each salt and pepper. Lower the heat to medium, and cook, stirring occasionally, until the tomatoes break down, 6 to 10 minutes.
Meanwhile, cook the orecchiette in the boiling water, stirring frequently until just tender, about 11 minutes. Reserve 1/2 cup of the cooking water and drain well. Return the pasta to the pot, add the sauce, and cook over medium-high heat, stirring, for 1 minute so the sauce and pasta meld. If the pasta seems dry, add enough cooking water to moisten it to your liking. Stir in half of the pecorino, season with salt and pepper to taste, and serve sprinkled with the remaining pecorino and basil.
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