Season both sides of the chicken breasts generously with salt and pepper. Place the flour in a shallow bowl or plate, then dredge each piece of chicken through it to form a light coating, shaking gently to remove any excess.

Add 2 Tablespoons of the butter and 2 Tablespoons olive oil to a large skillet set over medium-high heat. When butter melts, add the chicken and saute for 2-4 minutes per side, until cooked through and lightly golden. Remove the chicken to a plate, cover with foil, and set aside.

Add remaining 4 Tablespoons butter to the skillet. Allow the butter to brown and bubble, about 2-3 minutes, until it begins to give off a warm, nutty aroma.

Add garlic to the skillet, followed after just 30 seconds by the lemon juice, wine or broth, and about half of the basil leaves. Simmer the mixture for 2-3 minutes, scraping any browned bits from the bottom of the pan. Taste sauce and adjust with more salt and pepper, if desired.

When the sauce is slightly thickened, return chicken to the skillet to warm through. Top with remaining basil leaves, garnish with extra lemon wedges, and serve.