Cut the cutlets: Lay each chicken breast flat and slice it in half horizontally to make 4 thin cutlets, each about 1/2 inch thick. Pat them dry with paper towels, because a dry surface browns and a wet one steams.
Season and dredge: Whisk the flour, 2 teaspoons of the lemon pepper seasoning, the garlic powder, and the salt together on a wide plate. Press each cutlet into the mixture on both sides, then shake off the excess so only a thin coat stays.
Sear the chicken: Heat the olive oil in a large skillet over medium-high heat until it shimmers. Add the cutlets in a single layer and cook 4 to 5 minutes per side, until deep golden and an instant-read thermometer in the thickest part reads 165°F. Move them to a plate. Work in two batches if all four don't fit without touching.
Start the pan sauce: Reduce the heat to medium and add the butter to the same skillet. Once it melts, stir in the minced garlic and cook 30 seconds, just until fragrant.
Deglaze: Pour in the chicken broth and scrape the bottom of the pan with a wooden spoon to lift every browned bit. Simmer 2 to 3 minutes, until the sauce reduces by about a third and thickens slightly.
Finish with lemon: Take the skillet off the heat. Stir in the lemon zest, all of the lemon juice, and the remaining 1 teaspoon of lemon pepper seasoning. Taste and add a pinch more salt if it needs it.
Return the chicken and serve: Slide the cutlets and any juices from the plate back into the pan and turn them once or twice to coat in the lemon pepper sauce. Scatter the parsley over the top and serve right away with the extra sauce spooned over.
Notes
Slice the breasts into thin, even cutlets so they cook through evenly, and add the lemon juice off the heat so it stays bright instead of turning flat. Cook the chicken to an internal temperature of 165°F.