Slice the chicken breasts in half widthwise.
Place the sliced chicken breast one at a time into a plastic zip bag and gently pound it with a mallet or the bottom of a medium-sized pot.
Season the chicken breasts on both sides with salt and pepper and set them aside on a sheet tray lined with parchment paper.
In a shallow wide bowl or a cake or pie pan, add the flour and season it lightly with salt and pepper. Mix until combined.
Dredge the pounded seasoned chicken breasts in the seasoned all-purpose flour one at a time. Set them aside on a sheet tray lined with parchment paper.
Heat olive oil in a large frying pan over medium heat.
Cook the chicken for 3 to 4 minutes on each side until browned and cooked through. Set aside.
Add the sliced mushrooms to the pan and sauté until well browned.
Add shallots, garlic, and 1 tablespoon of butter to the pan. Stir and sauté for 1 minute.
Deglaze with white wine and cook until almost gone.
Remove the pan from the heat, add lemon juice and remaining butter. Mix until emulsified.
Stir in the cheese until creamy.
Season the sauce with salt and pepper, then place the chicken back in to heat it up.
Garnish with parsley, more cheese, and lemon zest.