Heat a medium nonreactive saucepan over medium-high heat. Add 1/3 cup of the oil and the garlic, and reduce the heat to medium. Cook the garlic, stirring often and mashing gently with a wooden spoon, until golden brown and beginning to soften, 5 minutes. Add the basil, tomatoes and their juices, the carrots and cheese rinds. Stir with a wooden spoon to combine. Bring to a simmer and adjust the heat to maintain a simmer. Cook for 35 minutes stirring occasionally to prevent sticking. Add 1 teaspoon of the salt. Remove from the heat and cool slightly.
Remove the rinds, carrots and basil. At this point you can use an immersion blender to puree slightly or leave it as a chunky sauce.
Bring a large pot of salted water to a boil. Cook the penne 2 minutes less than the package directions. Meanwhile, rewarm the sauce in a large, straight-sided skillet set over medium heat. Using a spider, strain the pasta from the water and add it directly into the pan with sauce, reserving 1/2 cup of the pasta water. Before stirring, sprinkle the pasta with the grated cheese. Toss the pasta, cheese and sauce together. Add the butter, the remaining 2 tablespoons olive oil and the reserved pasta water and continue to cook until the sauce is creamy and the pasta is al dente. Serve topped with more cheese if desired.