Place the chicken in a gallon freezer bag (or in between saran wrap) and use the textured side of a meat mallet to pound it to ½ inch thick.
Season with lemon pepper seasoning. You may also season with salt if desired.
Combine the flour, 1/4 cup of the Parmesan cheese, and garlic powder, on a large plate. Set aside.
Pat the chicken dry and dredge each side in the flour mixture. Tap off excess.
Heat olive oil in a large skillet over medium-high heat. Sear the chicken in batches for 4-5 minutes per side, until a golden crust has developed. Set aside and leave brown remnants in the pan.
Add the wine and garlic. Set heat to medium. Bubble gently for about 4 minutes, until the liquid has reduced by half. Use a silicone spatula to “clean” any remaining brown flecks on the pan while the wine reduces and incorporate it into the liquid for more flavor.
Add the chicken broth, chicken bouillon, and mustard powder. Bring to a gentle boil and let it simmer for 5 minutes or so, to thicken and concentrate the flavor. Reduce heat to low.
Add the half and half slowly, stirring continuously.
Stir in the lemon juice and slowly sprinkle in the 1 remaining 3/4 cup of Parmesan, stirring continuously, until combined. Add the chicken back and let the chicken warm through.
Optional: Swirl in 1 Tbsp. cold butter to give the sauce a smooth, velvety finish
