Flatten the chicken breasts into cutlets by butterflying each piece then placing them, one at a time, in a large zipper lock bag with small amount of water in it. Seal the bag, squeezing out as much air as you can. Pound out the chicken using a small cast iron skillet. As you finish each one, place them into a large plastic zipper bag or mixing bowl. Once all the breasts are pounded out, add the garlic paste to the bag or bowl and toss the chicken to coat. Marinate for about 10 minutes.
While the chicken is marinating, set up three pans on the counter. In one pan, add the flour, some salt and freshly ground pepper. In the second pan, beat the eggs with a couple teaspoons of water. In the third, combine the breadcrumbs, lemon zest, parsley and a handful of the grated Parmigiano-Reggiano (about 1/4 cup). Coat the cutlets by first tossing them in the seasoned flour, then dipping them in the beaten egg, then coating them in the breadcrumb mixture, pressing on each breast slightly to make sure everything sticks. Reserve the coated breasts on a plate.
Place two large skillets over medium-high heat, each with two turns of EVOO, about 2 tablespoons per pan. In one pan, cook the cutlets in batches until browned on each side and cooked through, 3-4 minutes per side. Keep the finished ones warm on a sheet pan in the warm oven. If necessary, add another tablespoon of oil to the pan between batches.
In the other pan, cook the peppers, onion and remaining garlic until tender, 6-7 minutes. Season the veggies with salt and freshly ground black pepper, then add the chicken stock and tomatoes, breaking them up with a wooden spoon or potato masher. Simmer the sauce until thickened, 4-5 minutes. Once thickened, stir in the torn basil and keep warm over low heat.
Once the sauce is about halfway done, drop the pasta into the boiling water and cook to al dente according to package directions. Drain the cooked pasta and return it to the pot it was cooked it along with the butter and remaining Parmigiano-Reggiano. Add about half of the prepared tomato sauce and toss everything together.
To serve, divide the pasta between your plates accompanied by one chicken cutlet per person. Divide the remaining sauce between the four plates.