Fill a large pot with water and bring it to boil. Add 1 tablespoon of rock salt and allow it to dissolve.
Add the Mezzi Paccheri pasta, which should takes about 10 minutes to cook (follow the time noted on your pasta packet). Give the pasta a quick stir to prevent sticking.
Heat a large pan over medium heat and add 6 tablespoons of EVOO.
Before the oil gets too hot, add a splash of water and the crushed garlic, then give it a stir.
Add the chopped chili and continue stirring for 30 seconds, then reduce the heat and add the halved cherry tomatoes.
Press down on the cherry tomatoes using a tomato crusher or the back of your wooden spoon.
Once the juice releases, increase the heat to medium-high and add the canned cherry tomatoes. Press them down and mix well.
Season with salt and pepper to taste, then tear half of the basil leaves by hand and add them in. Save the other half for later.
Lower the heat and stir frequently.
Once the pasta is almost ready, scoop up a mug full of pasta water and set it aside.
Taste the pasta to check if it is al dente (to your liking), if so, strain the pasta and add it to the sauce, stirring to combine.
-To thicken the sauce and create a more moist texture, add some of the reserved pasta water and toss.
Turn off the heat then add the grated pecorino and Parmigiano. Continue to toss the pasta until the cheese is well incorporated and serve right away.