Pound each chicken breast between plastic wrap to an even ½-inch thickness. Season both sides with salt and pepper.
Set up three shallow dishes: flour in one, whisked eggs and milk in the second, and breadcrumbs mixed with ½ cup Romano cheese in the third. Dredge each cutlet in flour, dip in egg wash, then press firmly into the breadcrumb mixture on both sides. Let rest 5 minutes.
Heat olive oil in a large oven-safe skillet over medium heat until shimmering. Fry the cutlets 3 to 4 minutes per side, until golden and cooked through (165°F internal). Transfer to a plate.
In the same skillet, melt the butter and add the garlic, cooking for 30 seconds. Stir in the roasted red peppers and crushed red pepper flakes. Add the white wine and simmer 1 minute. Stir in the heavy cream, chicken broth, and crushed tomatoes. Simmer 5 to 6 minutes until slightly thickened. Stir in the remaining Romano cheese and basil; season to taste.
Nestle the chicken back into the sauce, spooning sauce over each piece. Top each cutlet with a slice of provolone. Broil for 2 to 3 minutes, until the cheese is melted and browned in spots.
Meanwhile, cook the angel hair pasta in salted boiling water until al dente, about 3 to 4 minutes. Drain and toss with a spoonful of sauce from the skillet. Plate the pasta, top with a chicken cutlet, spoon extra sauce around the plate, and garnish with Romano cheese and basil.