In a bowl, season the flour with garlic powder, some sea salt & freshly cracked pepper, to taste; mix until well combined.
Whisk eggs until well combined in a separate bowl.
Cut the thin portion of the bottom couple of inches of the chicken breast off. Cut each remaining portion of the chicken breast in half lengthwise.
Place some plastic wrap over the top of the chicken on the cutting board, and pound with a mallet until they are about a ¼-½ inch thick.
Heat two tablespoons of olive oil in a large skillet over medium-high heat.
Dip the chicken lightly in the seasoned flour, then dip into the whisked egg, and lastly dip back into the flour before placing into the hot oil in the skillet; repeat with the remaining chicken, cooking in batches if needed.
Cook the chicken undisturbed until golden brown, about 4-5 minutes, then flip over and continue to cook until golden brown and cooked through, about 3-4 minutes.
Remove from the large skillet and place on a wire cooling rack. Cover loosely with a foil tent.
Add the remaining tablespoon of olive oil to the large skillet, then whisk in the flour until well combined. Cook while whisking, for 1-2 minutes.
Add the wine and minced garlic, then whisk until thickened, about 1 minute.
Slowly add the chicken broth and lemon juice while whisking; simmer for 2-3 minutes.
Whisk in the butter, then taste and season with sea salt and freshly cracked pepper, to taste. Add more lemon if needed.
Place the chicken on a serving platter, then drizzle with sauce and sprinkle the top with fresh parsley.