Fill a large pot with 6 quarts water and bring to a boil.
Pour the 3 tablespoons extra-virgin olive oil in a 12-inch skillet, add the 1 medium clove garlic and 1/4 teaspoon hot red pepper flakes , and place over medium-high heat. Cook, stirring, until the garlic is sizzling.
Add the 1 3/4 pounds fresh tomatoes, season with salt, and cook until the tomatoes release their liquid and it evaporates, 10 to 12 minutes.
While the tomatoes are cooking, cut the salmon into strips about 1/4 inch thick and 1 1/2 inches long.
When the tomato liquid has evaporated, add about 2 tablespoons salt to the boiling pasta water and then add the 1 pound farfalle, penne, or fusilli. Stir well and cook until al dente.
While the pasta is cooking, add the 1/2 pound salmon fillet to the tomatoes, season with salt, and add the 3/4 cup heavy cream.
Coarsely chop or rip the 6 to 8 basil leaves and add them to the skillet. Cook until the cream has thickened and reduced by about 1/3, 2 to 3 minutes.
When the pasta is done, drain well, toss it with the salmon sauce, and serve at once.