Rinse and pat dry chicken.
Whisk together egg, parmesan cheese, parsley, salt, and pepper until frothy and thick.
Spread flour on a plate. Coat the chicken with the flour and shake off the excess.
Heat oil and butter in a large skillet over medium-high heat.
Dip the floured chicken into the egg batter and place in the hot pan. Cook in batches, being careful not to crowd the pan.
Cook until nicely browned about 2 minutes on each side. Repeat, adding more oil and butter as needed, until all the chicken slices are cooked. Remove to a platter and keep warm.
Saute garlic in butter in the same large skillet.
Stir flour in cold water; then add to skillet.
Add lemon juice, as well. Continuously stir over medium-high heat to thicken gravy about 2 minutes.
Return chicken to the pan and cook for 1 minute to blend. Season with salt and pepper to taste. Garnish with parsley and lemon wedges. Serve immediately with your favorite gluten free pasta.