Place chicken breasts on a cutting board. Using a sharp knife held parallel to the board, butterfly each breast by cutting through the middle lengthwise, leaving one edge intact so the breast opens like a book.
Divide the butter into four portions (about 1½ tablespoons each). In the center of each opened breast place a portion of butter, 1 teaspoon chopped parsley, a small pinch of minced garlic, and a sprinkle of lemon pepper seasoning.
Fold the breasts closed over the filling and press the edges firmly to seal.
Set up three shallow pans: whisk the eggs in one, place the panko in a second, and combine the flour and salt in the third.
Heat about 3/4 inch of oil in a large skillet over medium heat until shimmering but not smoking.
Working one at a time, dredge each sealed breast in the flour mixture, then dip thoroughly in the beaten eggs to coat completely, and finally press into the panko to form an even crust.
Carefully place the breaded breasts in the hot oil and cook for 4–5 minutes per side, flipping gently once, until golden brown and cooked through.
Transfer the cooked breasts to a paper towel–lined plate to drain briefly, then serve warm.
