In a large saucepan add the olive oil and garlic. Saute over medium-high heat for 2-3 minutes or until the garlic is golden brown. Add in the canned tomatoes, red pepper flakes, carrots, and parmesan rinds.
Lower the heat to low and simmer the sauce for 20 minutes. While the sauce is simmering break up the tomatoes with the back of a wooden spoon.
After the sauce simmers remove the carrot pieces and rinds. Add in the basil, butter, and salt and pepper simmering for 2-3 more minutes. Blend the sauce with an emulsion blender or food processor until well blended. If you prefer, a more chunky sauce you can skip this step.
Add in the ½ cup of pasta water and the bucatini noodles to your sauce and toss well. Top your pasta with grated parmesan cheese and basil.