If your chicken breasts are thick, place them between two sheets of plastic wrap and pound gently with a meat mallet or rolling pin until they are about 1/2 inch thick. You want even thickness so the whole cutlet cooks at the same rate. Season both sides with salt and pepper.

Spread the flour in a shallow dish. Dredge each cutlet in the flour, pressing lightly so it sticks, then shake off the excess. You want a thin, even coat, not a heavy crust.

Heat the olive oil and 2 tablespoons of butter together in a large skillet over medium-high heat. When the butter foam subsides and the pan is hot, add the cutlets in a single layer. Do not crowd the pan. Work in two batches if needed. Cook for 3 to 4 minutes without moving, until the bottom is deep golden and releases easily from the pan. Flip and cook another 2 to 3 minutes. The internal temperature should reach 165 degrees F. Transfer the cooked cutlets to a plate and tent loosely with foil.

Reduce the heat to medium. Wipe out any dark bits from the pan with a paper towel, but leave the pan on the heat. Add the remaining 2 tablespoons of butter. Once the butter melts and begins to foam, add the sage leaves in a single layer. Let them fry in the butter undisturbed for about 45 seconds to 1 minute until they turn crisp and the butter around them smells nutty and toasty and turns a light amber color. Watch it closely. It moves from perfect to burnt very fast.

The moment the butter is golden brown and fragrant, pull the pan off the heat. Add the garlic (if using) and stir for 15 seconds using the residual heat. Add the lemon juice carefully, as it may sputter. Taste the sauce and add a small pinch of salt if needed.

Arrange the cutlets on a serving platter or individual plates. Spoon the brown butter and crispy sage leaves evenly over the top. Serve immediately while the sage is still crisp. Buttered pasta, roasted sweet potatoes, or a simple green salad all work great alongside.