Bring a large pot of salted water to a rolling boil.
In a large skillet, heat the olive oil over medium-high heat. Add the guanciale, reduce the turn heat to medium, and saute until crisp and browned, 6 minutes.
While the guanciale is cooking, blend the pelati in a blender until smooth.
Add the garlic and red pepper flakes to the skillet with the guanciale, and cook until golden brown, about 1 minute. Add the pureed tomatoes, basil, salt, and pepper. Reduce heat to medium-low and simmer for 15 minutes.
Add the bucatini to the pot of boiling water and cook for 1 minute less than the time indicated on the package. Drain the bucatini, add it to the sauce, and toss. Serve immediately with plenty of grated pecorino and a sprinkling of chopped parsley.