Place each chicken breast between two sheets of plastic wrap and pound to about 1/4-inch thickness, or slice thick breasts in half horizontally to make even cutlets.
Season the flour with salt and pepper in a shallow bowl.
In a second shallow bowl, whisk together the egg and water until combined.
On a plate, combine the gluten-free breadcrumbs, dried Italian seasoning, and garlic powder.
Dredge each chicken cutlet first in the seasoned flour, shaking off excess, then dip into the egg mixture, and finally press into the breadcrumb mixture to fully coat.
Heat a thin layer of olive oil in a skillet over medium heat until shimmering.
Cook the coated cutlets in the skillet for about 3–4 minutes per side, flipping once, until golden brown and an instant-read thermometer inserted into the thickest part reads 165°F (74°C).
Transfer cooked cutlets to a paper towel-lined plate to drain briefly, then garnish with fresh parsley and serve with lemon wedges if desired.