Heat 1/3 cup olive oil in a large pot over medium heat until shimmering.
Add 5 smashed garlic cloves and cook 2–3 minutes, until lightly golden and fragrant.
Stir in the 6 finely chopped heirloom tomatoes and any juices, then add 1 cup fresh basil, the carrot cut into four, and the parmesan rinds.
Reduce or adjust heat to maintain a gentle simmer and cook, stirring often, 30–40 minutes until the sauce thickens; season with 1 teaspoon kosher salt.
While the sauce simmers, bring a large pot of salted water to a boil and cook 1 pound penne until al dente; reserve 1/2 cup pasta cooking water and drain the pasta.
When the sauce is done, remove and discard the whole garlic cloves and carrot pieces. If desired, puree the sauce in a blender or with an immersion blender for a smoother texture, or leave it chunky.
Return the sauce to the pot off the heat and stir in 1/2 cup grated parmesan, 4 tablespoons room-temperature butter, and the cooked penne; toss to combine.
Season to taste with black pepper and a pinch of crushed red pepper flakes; thin the sauce with reserved pasta water if needed.
Divide the pasta among bowls and top each with 1 cup whole milk ricotta (divided), halved cherry tomatoes, and additional basil; serve immediately.