Place 6 quarts water to boil and add 2 tablespoons salt
In a 12 to 14-inch saute pan, place tomato sauce and tomatoes and bring to a boil. Lower heat to simmer and add basil leaves without stirring. Cook pasta according to package instructions, until just short of "al dente". Drain in colander and toss into pan with tomatoes and basil. Add mozzarella pieces and toss over medium heat until cheese is just melting. Pour into warm bowls and serve immediately.
Saute the onion and garlic in the olive oil over medium heat until translucent, but not brown (about 10 minutes). Add the thyme and carrot and cook 5 minutes more. Add the tomatoes. Bring to a boil, lower the heat to just bubbling, stirring occasionally for 30 minutes. Season with salt to taste. Serve immediately, or set aside for further use. Thesauce may be refrigerated for up to one week or frozen for up to 6 months.