Prep everything first. Set up the flour and egg batter, mince the garlic, drain the capers, cut the butter into pieces, and measure the wine and chicken stock. Slice half of the lemon into thin rounds and juice the remaining half. Once cooking starts, this recipe moves quickly, so having everything ready makes it much easier.
Prepare the chicken. Butterfly two thick chicken breasts or pound chicken to about ¼-inch thickness. Season both sides generously with salt and pepper.
Make the egg batter and dredging station. In a shallow bowl, whisk together the eggs, cream or milk, Parmesan cheese, Italian seasoning, salt, and pepper until smooth and slightly frothy. Place the gluten-free flour in a separate shallow bowl or plate. The flour does not need to be seasoned.
Heat olive oil in a large skillet over medium-high heat until hot and shimmering. A small piece of gluten-free bread should sizzle immediately when added. This is very important, you need the oil to be hot or the batter will stick the pan.
Cook the chicken. Dredge each cutlet lightly in flour, dip into the egg batter, and place into the hot oil. Cook two cutlets at a time for 4–5 minutes per side, until golden and cooked through (internal temperature should reach 165°F). Transfer to a plate.
Wipe out the pan. Carefully discard excess oil and wipe out the skillet with paper towels to remove browned batter bits. This helps keep the sauce clean and prevents bitterness.
Start the piccata sauce. Return the pan to medium heat and melt 2 tablespoons of butter. Add the lemon slices and cook for 1–2 minutes per side, until lightly browned. Remove the lemon slices and set aside.
Add the garlic and capers to the pan and cook for 30–60 seconds, just until fragrant. Do not let the garlic brown.
Add the white wine, rest of the butter, and reserved lemon juice. Increase heat to medium-high and simmer for about 5 minutes, allowing the wine to reduce slightly and cook off the alcohol.
Pour in the chicken stock and simmer for 6–8 minutes (up to 10 minutes), until the sauce reduces by about half. Be patient with this step.
Reduce heat to medium-low and return the chicken to the pan. Spoon the sauce over the chicken and cook for about 3 minutes, just until heated through.
Transfer the chicken to a platter or plate and spoon the sauce over the chicken. Place the lemon slices on top.