Prepare biscuits according to package directions.
If frying, heat peanut oil in pressure cooker to 400°F. If baking or air frying, preheat to 375°F.
Pound chicken breasts flat and cut each in half to make 4 large pieces. In a large zip to lock bag, combine pickle juice and ¼ cup water. Add chicken and marinate for 30 minutes.
In a flat bowl combine 1 egg and milk thoroughly. In another bowl combine flour, powdered sugar, pepper and salt. Dip each piece of chicken in the egg/milk mixture, then coat with the flour mixture, then place gently in the hot oil (or on a baking sheet or in air fryer).
Pressure Cooker: close pressure cooker, bring to pressure, cook for 3½ minutes, do a quick release and remove chicken to paper towels to drain. Air Fryer: air fry for 7-10 minutes, flipping half way through cooking time. Baking: bake 10-15 minutes, flipping half way through cooking time.
While the chicken is cooking, heat a small amount of oil in a large skillet. Scramble remaining 4 eggs in a bowl. Pour in the hot skillet and cook without stirring just until cooked through.
Remove egg from pan and cut into 4 pieces.
Cut biscuits in half, add a piece of chicken, egg, and cheese to each. Serve immediately while warm.