Place chicken breasts between plastic wrap and pound thick areas until as thin as the thinnest areas.
Roll up each piece of cheese in each slice of ham.
Center each roll on each chicken breast; roll chicken around ham roll, folding sides in; hold chicken rolls together using toothpicks.
Mix Panko, Parmesan cheese, salt, pepper, flour and paprika in a shallow pan; whisk egg to frothy in a separate bowl; dip each rolled chicken breast in egg, then Panko mixture; set aside.
Melt butter in a large skillet over medium-high heat; sear and turn chicken rolls until browned on all sides.
Pour chicken broth into the skillet; reduce heat to low, cover, and simmer for ~20 minutes.
Transfer chicken breasts to a warm platter and remove toothpicks.
Whisk half & half into sauce in skillet; cook, stirring until thickened.
Nutrition Facts: Servings: 8; Amount per serving: Calories 456; Total fat 33.2g 51%; Saturated fat 7.4g 37%; Cholesterol 111mg 37%; Sodium 601mg 25%; Carbohydrates 18.6g 6%; Fiber 1g 7%; Sugars 8g 16%; Protein 20.6g 41%; Based on DV of 2000 calories per day
Chicken Kiev Substitute ham and Swiss cheese (steps 2 and 3) with garlic butter stuffing (see below); mix all together; form four equal logs in plastic wrap and chill; proceed with steps 3 through 9. Kiev garlic butter: stuffing (per chicken breast): 3 oz butter, softened; 1 tablespoon fresh parsley, chopped fine; 2 cloves garlic, minced