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 bottom few inches from the chicken breast. Cut each remaining portion of the chicken breast in half lengthwise.
Place plastic wrap over the chicken on the cutting board, and pound with a mallet until about 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 finally, dip back into the flour before placing in 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 and continue to cook until golden brown and cooked through, about 3-4 minutes.
Remove from the large skillet and place on a wire 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, for about 1 minute.
Slowly whisk in the chicken broth and lemon juice, and 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.