Start by patting the chicken dry and seasoning with salt and pepper. Set up three dishes for flour, beaten eggs, and breadcrumb-Parmesan mixture. Coat chicken first in flour, then egg, then crumbs, pressing gently so coating sticks well.
Heat butter and olive oil in a skillet over medium heat until hot. Cook chicken in batches to avoid overcrowding, allowing each side to become deeply golden. Remove cooked chicken and keep warm while preparing the sauce.
In the same skillet, sauté minced garlic briefly until fragrant. Add wine to deglaze, scraping flavorful bits from the pan. Stir in cream, Italian seasoning, and chili flakes, then simmer until thick and creamy.
Return chicken to the skillet so it warms in the sauce. Spoon sauce over each piece and simmer briefly so flavors combine. Finish with chopped parsley and serve immediately.