Place the chicken breasts between two sheets of plastic wrap and pound or roll them to 1/4-inch thickness; if very thick, slice each breast horizontally into two even cutlets.
Season the flour with salt and pepper in a shallow bowl.
In a second shallow bowl, whisk the egg with the tablespoon of water until combined.
In a third shallow plate or bowl, mix the gluten-free breadcrumbs with the dried Italian seasoning and garlic powder.
Dredge each chicken cutlet first in the seasoned flour, shaking off excess, then dip into the egg wash, and finally press into the breadcrumb mixture to coat evenly on both sides.
Heat a thin layer of olive oil in a skillet over medium heat until shimmering.
Cook the coated cutlets 3–4 minutes per side, flipping once, until golden brown and the internal temperature reaches 165°F (74°C).
Transfer cooked cutlets to a paper towel-lined plate to drain briefly.
Serve warm, garnished with fresh parsley and lemon wedges if desired.