Warm 1.5 tbsp olive oil in a saucepan over medium heat. Sauté garlic until fragrant, about 30 seconds.
Stir in roasted peppers, smoked paprika, and red pepper flakes. Cook 2 minutes, stirring often.
Pour in broth and cream. Simmer 3–4 minutes, then blend until smooth. Season with a pinch of salt and the lemon juice. Keep warm.
Pound chicken to 1/4-inch thickness if needed. Season both sides with 1 tsp salt and the black pepper.
Set up three dishes: flour; beaten eggs; panko mixed with Parmesan and lemon zest.
Dredge each cutlet in flour, shake excess. Dip in egg, then press into panko mixture to coat well.
Heat 3 tbsp oil in a large skillet over medium-high. Fry half the cutlets 2–3 minutes per side until deep golden and 165°F.
Transfer to a rack and sprinkle lightly with salt. Repeat with remaining oil and cutlets.
Spoon pepper sauce onto plates. Top with chicken and parsley. Serve right away.