Bring pasta water to a boil with a generous pinch of salt.
Heat your pan over medium heat. Once heated, add the olive oil and lay the mortadella flat in the pan.
Add the radiatori pasta to the pasta water.
Once the bottom of the mortadella has browned, use a spoon to stir and flip the meat until all sides are brown. Once all sides are brown, reduce the heat to low.
Cook the pasta to about a minute less than the instructions on the bag or box. Two minutes before the pasta is finished, reserve about a 1/2 cup of the pasta water in a heatproof measuring cup and set aside.
Turn the heat on the mortadella to medium. Once heated, pour about half the pasta water into the pan with the mortadella and cook until it reduces into a starchy liquid. If you run a wooden spoon across the bottom of the pan, you should be able to see the surface of the pan.
Once the pasta is cooked, lift the pasta from the pot with a slotted spoon or strain it into a colander. Add the pasta to the pan with the mortadella. Stir the pasta and the mortadella until the mixture is slightly thick and a bit starchy - about one to two minutes. Turn off the heat and let the pan stand on the same burner for about 3 minutes.
After 3 minutes, immediately add the pesto and mix until incorporated. Add a small amount of the remaining pasta water if the mixture feels too tight and not saucy enough. Sprinkle in grated cheese until the dish becomes slightly thick. Serve in flat pasta bowls and garnish with additional parmigiano and torn basil leaves.
Notes
You can substitute Grand Padano or any good parmesan cheese if you don't have Parmigiano-Reggiano.