Cut the butterflied and pounded breasts into 6 to 8 even pieces. Season with the salt on both sides and place on a rack set inside a sheet pan (technically we use "half" sheet pans for this). Cover and refrigerate for 30 minutes.
Combine the breadcrumbs, potato chips, oregano, parsley, and garlic powder in a 1 gallon zip-top bag and crush into a course meal.
Set up a breading station with three loaf pans: Place the flour in the first pan, the beaten eggs in the second, and the breadcrumb mixture in the third. Set a clean wire rack inside a sheet pan to hold the breaded pieces.
Unwrap the chicken and blot well with paper towels then dredge the chicken first in the flour (shake off the excess), then dip in the beaten eggs (again, drain the excess), and finally coat with the breadcrumbs before placing on the rack.
Position an oven rack in the top third of the oven and crank the broiler to high. Line a clean pan with paper towels and have it standing by.
Melt 2 tablespoons of the butter with 1 tablespoon of the olive oil in an 11-inch sauté pan over medium heat. When the butter foams, add half the breaded chicken to the pan, but don’t overcrowd. Cook, undisturbed, until crisp and golden brown, about 2 minutes per side. Transfer to the clean rack, wipe out the pan, and repeat with the remaining butter, oil, and chicken.
Spread 3/4 cup of the red sauce into the bottom of a a 9-by-13-inch broiler-safe baking dish or pan and broil until the sauce bubbles and begins to caramelize, about 2 minutes.
Remove the dish from the oven and arrange the chicken pieces in a single layer. Dot the chicken with the remaining red sauce, leaving bare spots to retain some crispy bits. Scatter the fontina and mozzarella over the sauce.
Return to the broiler until the cheese is bubbly and beginning to brown, about 1 minute to 1 minute and 30 seconds.
Garnish with chopped flat-leaf parsley.