Over medium heat, sauté carrot in olive oil until soft. Then add the onion and cook until they turn translucent. Throw in the garlic and let it cook for about a minute.
Add the tomatoes, basil, salt, and pepper. Cook covered over low heat for about five minutes, or until the sauce starts to bubble a little. Don't let it cook for too long or it won't taste fresh!
*The carrot makes this sauce pretty sweet, but if you want it even sweeter toss some frozen peas in towards the end.