Heat the olive oil in a large pot set over medium heat. Add the garlic and cook for 2-3 minutes or until lightly caramelized and fragrant. Slowly add the tomatoes and any juices left on your cutting board. Add the basil, carrots and parmesan rind. Adjust the heat to medium to keep the sauce at a simmer. Simmer for 30-40 minutes until the sauce has thickened. Stir often to avoid sticking. Stir in the salt.
Meanwhile, bring a large pot of salted water to a boil. Boil the pasta until al dente. Reserve 1/2 cup of the pasta cooking water. Drain.
Once the sauce has thickened, you can either puree the sauce in a blender or leave it chunky. Remove from the heat, remove the whole garlic cloves and carrots from the sauce. Stir in the pasta, parmesan cheese and butter. Toss to combine. Season to taste with salt, pepper and crushed red pepper flakes. If needed, thin the sauce with pasta cooking water. Divide the pasta among bowls and top with ricotta cheese, black pepper, cherry tomatoes and basil. EAT!
*Adapted from [Food Network | http://www.foodnetwork.com/recipes/giada-de-laurentiis/basic-parmesan-pomodoro.html].