Line 2 large baking sheets with parchment paper or wax paper. Halve each tomato and place cut side up in 1 flat layer on the baking sheets. Put a slice of garlic on top of each tomato half. 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(be careful not to burn the garlic). I check after about a 1/2 hour and push the garlic down into the tomato.
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. Enjoy!