Pat the chicken dry with paper towels. Cut each breast in half horizontally to create 4 pieces, then pound each to about 1/4-inch even thickness. Season both sides generously with salt and pepper.

In one shallow bowl, whisk together the flour, garlic powder, and paprika. Set aside 2 tablespoons of this seasoned flour for the sauce. In a second bowl, whisk the egg with 2 tablespoons of lemon juice squeezed from one half of the lemon.

Melt 1 tablespoon of butter with the olive oil in a large cast-iron skillet over medium-high heat until the butter foams and the foam begins to subside.

Working in batches, dredge each chicken piece in the seasoned flour on both sides, dip in the egg wash letting excess drip off, then add to the hot skillet. Do not overcrowd the pan.

Fry each piece for 2 minutes per side until deep golden and the coating looks set. Transfer to a plate and set aside.

Reduce the heat to medium. Melt the remaining 2 tablespoons of butter in the same skillet. Stir in the reserved 2 tablespoons of seasoned flour and the minced garlic. Cook for 30 seconds, stirring constantly so the garlic does not burn.

Pour in the white wine and deglaze the pan, scraping up any browned bits from the bottom. Let reduce for 1 to 2 minutes until the sharp alcohol smell mellows.

Whisk in the chicken broth and remaining lemon juice from the used lemon half. Simmer for about 2 minutes, whisking steadily, until the sauce thickens slightly and coats the back of a spoon.

Reduce the heat to medium-low and nestle the chicken back into the pan. Lay the lemon slices cut from the second lemon half on top. Cover and simmer gently for 3 to 5 minutes until the chicken reaches an internal temperature of 165 degrees F.

Taste and adjust salt and pepper as needed. Garnish with fresh chopped parsley and serve immediately straight from the pan.