Pat the chicken breasts dry with paper towels. Slice each breast in half butterfly-style, but cut all the way through. Pound each chicken breast half to an even thickness of about 1/4 inch. (This also tenderizes the chicken, so don’t be shy.)

In a large rimmed dish, mix together the flour, 1 1/2 teaspoons of the salt, and the pepper.

Crack the eggs into another rimmed dish and beat together with the milk and remaining 1/2 teaspoon salt.

In a 12-inch skillet, warm the olive oil over medium-high heat until it shimmers.

Dredge each chicken piece in the flour mixture until thoroughly coated and then in the egg wash. Add directly to the pan. In a 12-inch skillet you’ll likely be able to cook three pieces of chicken at a time. (Dredge each piece immediately before cooking.)

Cook for about two to three minutes, depending on thickness, until golden brown underneath and beginning to show signs of cooking halfway through. Flip and cook for another minute or two until chicken is just about cooked through. You can adjust the heat as necessary to cook the chicken through while browning but not burning. Remove from pan and set aside on a plate.

Repeat until all chicken breasts are cooked.

Slice one of the lemons into thin slices and remove seeds. Add lemon slices to pan in a single layer and cook until lightly caramelized on the underside, then flip and repeat. Remove from pan and set aside with the chicken.

Add the wine to the pan. Scrape up any brown bits and stir into wine. When wine has reduced by half, add chicken broth.

In a small bowl, mash together the softened butter with 1/4 cup of the leftover dredging flour mix to form a smooth paste. Add this beurre manie to the pan and whisk into the sauce until no lumps remain.

Juice the remaining lemon and strain two tablespoons of the juice into the pan. (You can use more if you like a very lemony flavor.)

Bring to a boil, then reduce heat and simmer briskly until glossy and gently thickened, about five minutes.

Return chicken and lemon slices to the pan and simmer to re-warm. Season with additional salt and pepper if you like.

Off the heat, sprinkle with parsley and serve.