Line 2 large baking sheets with parchment paper. Halve each tomato and place cut side up in 1 flat layer on the baking sheets. Drizzle the tomatoes with 1 tablespoon of the olive oil and sprinkle on the salt. Roast until the tomatoes are dried around the edges but still moist, about 2 hours.
Crumble the goat cheese into large chunks and refrigerate until ready to serve the pasta.
Cook the pasta in salted boiling water according to the package directions. Remove 1 cup of the cooking liquid and reserve. Drain the pasta well and return to the pot. Add the tomatoes, goat cheese, basil, reserved cooking liquid, and remaining 2 tablespoons olive oil. Toss well and season with salt and pepper. Serve warm.