Bring a large pot of water to a boil. In a large frying pan over medium heat, warm the oil. Add the garlic and sauté until fragrant, about 1 minute. Add the tomatoes and cook, stirring often, until they give off their juices, about 3 minutes. Add the chopped vegetables and cook, stirring frequently, until heated through, about 5 minutes. Season to taste with salt and pepper. Reduce the heat to low to keep warm.
Cook the pasta
Add 2tablespoons salt and the pasta to the boiling water. Cook, stirring occasionally to prevent sticking, until al dente, according to the package directions. Drain, reserving about ½ cup (4fl oz/125ml) of the cooking water. Return the pasta to the pot. Add the vegetables, goat cheese, and basil and toss to combine. Add as much of the cooking water as needed to achieve a nice coating consistency for the sauce. Cook briefly over low heat to blend the flavors. Serve, passing the Parmesan cheese at the table.