Bring a large pot of water to a boil over high heat.
Add the pasta and 1 tablespoon of the salt and return to a boil. Cook, stirring occasionally, until al dente, about 15 minutes.
Using oven mitts or pot holders, remove the pot of pasta from the heat and drain the pasta away from you into a colander set in the sink. Return pasta to the pot but keep off the heat.
While the pasta is cooking, cook the sausage in a large skillet over medium-high heat, stirring until evenly browned and cooked through, about 7 to 8 minutes.
Add the onion and cook, stirring, until golden brown around the edges, about 8 to 10 minutes.
Add the garlic, the remaining teaspoon of salt, and the pepper and cook, stirring, for 30 seconds.
Add the sausage mixture to the pasta. Add the olive oil and the basil, and toss to coat evenly.
To serve, divide equal portions of the pasta mixture among plates or soup bowls. Garnish each serving with equal portions of the Parmesan cheese.
YIELD: 6 to 8 servings