Heat an outdoor grill or indoor grill pan to high. Season the chicken with salt and pepper, and drizzle with EVOO to keep it from sticking to the grill. Cook for 3-4 minutes on each side and transfer to a foil-covered platter to hold. If you are using a grill pan, cook the chicken in 2 batches if necessary. While the chicken cooks, make the sauce.
Place a medium pot on the stove over medium heat. Add 2 tablespoons of the EVOO (twice around the pan). Add the garlic, red pepper flakes and onion. Cook for 10 minutes, stirring often. Add the tomatoes and heat through, 2 minutes. Wilt in the basil and season the sauce with salt and pepper.
Preheat the broiler to high.
Layer the chicken with the tomato sauce in a casserole dish. Top the casserole with Parmigiano and mozzarella. Brown the chicken parm casserole under the broiler for 3 minutes. Meanwhile, prepare the salad.
Place the greens in a salad bowl. Dress with the vinegar and the remaining 3 tablespoons of EVOO. Season with salt and pepper to taste.
Serve the chicken parm alongside a little salad.