Season both sides of chicken with salt and pepper.
Place flour on a plate. In a shallow bowl, whisk together egg and water. Place bread crumbs on a second plate.
Coat both sides of chicken in flour, dip in egg mixture, and then coat with bread crumbs.
Place butter and oil in a large pan and heat over medium-high heat.
Add chicken and cook for about 3 to 4 minutes per side. Remove chicken to a plate and set aside.
Add garlic to drippings left in pan. Cook 1 minute.
Add chicken broth and heavy cream to pan. Simmer 2 to 3 minutes.
Add lemon juice and cornstarch mixture. Simmer 1 minute.
Add Parmesan cheese and capers to pan.
Return chicken to pan. Remove from heat and serve over pasta or mashed potatoes.