Pound each breast portion down to 1/4-inch between 2 sheets of plastic wrap using a mallet.
Dip each breast in the cream, allowing excess cream to drip off.
Bread each breast with the bread crumbs and place on a cooling rack (like you use for cookies) to allow the breading to dry slightly and adhere better, about 10 minutes.
FOR DEEP FRY ONLY--heat oil to 350 degrees F. Fry for 5 minutes total. I was able to fry 2 breasts at a time, but this will probably have to be done in shifts so you can keep the cooked pieces warm by placing them on a cooling rack and placing them in a 200 degree F oven. Repeat until all chicken is cooked.
TO SAUTE IN A PAN--Heat 1 tbs olive oil in a large skillet over medium heat. Brown breasts well. about 5 minutes per side. Keep warm as instructed in the deep fry section. Repeat with remaining chicken.
TO MAKE SAUCE--Melt butter in a large sauce pan over medium heat.
Saute onion, garlic and peppers until aromatic--about 2-3 minutes.
Empty can of soup into the saucepan. Whisk in milk gradually so the sauce is smooth. Heat through.
Add the softened cream cheese and the Parmesan cheese. Cook, stirring, until cream cheese is melted.
Turn off heat and add shredded cheddar. Stir until melted. Add any salt or pepper at this point if you need it.
Place chicken on serving platter and drizzle sauce over chicken or serve the sauce separately as gravy so each person can add their own.