Begin by ensuring that each chicken breast half is of even thickness, ideally pounded to approximately ¼ inch. This ensures uniform cooking and optimal texture.

In a shallow dish, whisk together the egg substitute, two tablespoons of dry white wine, two tablespoons of fresh lemon juice, minced garlic, and hot pepper sauce. In a second shallow dish, combine the all-purpose flour, grated Parmesan cheese, minced parsley, and kosher salt.

Dredge each piece of chicken in the flour mixture, then dip it into the egg mixture, and finally, dredge it once more in the flour mixture to ensure an even and thorough coating.

In a large nonstick skillet, heat 1½ teaspoons of olive oil over medium heat. Place four of the prepared chicken breast halves into the skillet and cook for approximately 3 to 5 minutes per side or until golden brown and the internal temperature reaches 165°F (74°C). Transfer the cooked chicken to a warmed plate and cover lightly with foil to maintain warmth. Discard any remaining drippings from the skillet.

In the same skillet, melt the unsalted butter over medium heat. Add the remaining ¼ cup of dry white wine and the remaining three tablespoons of fresh lemon juice. Bring the mixture to a gentle boil and cook uncovered until the sauce reduces by one-fourth, intensifying its flavor.

Place the cooked chicken breasts on a serving platter and spoon the lemon sauce over the top. Garnish with additional minced parsley if desired. Serve immediately.