1. In a large pot of boiling salted water, cook the pasta until al
dente. Drain the pasta, reserving 3/4 cup of the cooking water.
2. Meanwhile, in a large, deep skillet, heat 1 tablespoon of the olive
oil until shimmering. Add the sausage in 1-inch clumps and cook
over moderately high heat, turning once, until browned and cooked
through, about 8 minutes. Using a slotted spoon, transfer the
sausage to a plate.
3. Add 2 tablespoons of the olive oil to the skillet along with the
tomatoes and crushed red pepper; cook over moderately high heat,
pressing the tomatoes until slightly softened, about 4 minutes.
Add the reserved pasta cooking water, season with salt and cook
over moderate heat, scraping up any browned bits and crushing
the tomatoes, until the liquid is reduced by half and the tomatoes
are nearly broken down, about 5 minutes.
4. Add the pasta to the skillet along with the sausage and the
remaining 1 tablespoon of olive oil and cook, stirring, until the
pasta is evenly coated, about 3 minutes. Remove from the heat
and stir in the provolone. Transfer to bowls and serve right away.