Slice each chicken breast in half lengthwise to make 4 thin cutlets; season both sides with salt, pepper, and garlic powder.
Lightly dredge each cutlet in flour, shaking off excess, and set them aside on a plate.
Heat a large skillet over medium-high heat and add the olive oil and 1 tablespoon butter; when the pan is hot, add the chicken cutlets in a single layer.
Sear the chicken until golden, about 4–5 minutes per side, until nearly cooked through; transfer the cutlets to a plate and keep any juices on the plate.
Reduce heat to medium, add the remaining 2 tablespoons butter to the skillet, then sprinkle in the reserved 1 tablespoon flour and cook, stirring, for 30 seconds to 1 minute.
Whisk in the chicken broth until smooth and no lumps remain, then stir in the grainy mustard, Dijon, and honey until the sauce is combined.
Return the chicken and any collected juices to the pan, reduce heat to a gentle simmer, and cook for another 4–5 minutes until the chicken reaches 165°F and the sauce has thickened slightly.
Taste and adjust seasoning with salt and pepper if needed, then serve immediately sprinkled with chopped parsley if desired.