Pound & dredge the cutlets: Place the halved chicken breast cutlets between two sheets of parchment paper. Gently pound them with a meat mallet to an even 1/3-inch thickness. In a shallow bowl, whisk together the flour, grated Parmesan, garlic powder, salt, and black pepper. Dredge each cutlet thoroughly in the flour mixture, shaking off any excess coating.

Pan-sear to golden perfection: Heat 2 tablespoons of olive oil and 1 tablespoon of butter in a large heavy skillet (preferably cast-iron or stainless steel) over medium-high heat until shimmering and hot. Add cutlets in a single layer (work in batches if needed). Sear for 3 to 4 minutes per side without moving until golden-brown, crispy, and cooked through (internal temp reaches 165°F / 74°C). Transfer cutlets to a warm plate and tent lightly with foil.

Sear lemon slices & aromatics: In the same hot skillet, add lemon rounds and sear for 1 minute per side until caramelized. Remove to the chicken plate. Lower the heat to medium, add 1 tablespoon of butter and minced garlic, sautéing for 30 to 45 seconds until fragrant and golden.

Deglaze & simmer pan sauce: Pour in chicken broth (or white wine), scraping up all the savory browned bits (fond) stuck to the bottom of the skillet. Stir in lemon juice and capers. Bring to a rapid simmer and let reduce by half, about 3 minutes.

Mount sauce & finish: Remove the skillet from heat. Whisk in the remaining 2 tablespoons of cold butter one piece at a time until the pan sauce emulsifies into a glossy, velvety consistency. Stir in minced fresh parsley and fresh thyme.

Spoon sauce & serve: Return the crispy chicken cutlets and seared lemon slices to the skillet or arrange on a serving platter. Spoon the warm, bubbling lemon garlic herb butter sauce generously over the top. Serve immediately with pasta, crusty bread, or roasted veggies!