Place chicken cutlets between plastic wrap and pound to an even thin thickness; season both sides with salt and pepper.
Put the flour on a shallow plate and dredge each cutlet, shaking off excess flour.
Heat 1–2 tablespoons olive oil in a large skillet over medium heat. Add the chicken and cook until golden brown on both sides, about 3–4 minutes per side; transfer to a plate and set aside.
Remove the pan from heat, add the minced garlic to the pan and stir briefly until fragrant, about 20–30 seconds, being careful not to burn it.
Return the pan to medium-high heat and add the chicken broth, scraping up any browned bits from the bottom. Bring to a gentle boil and let the sauce reduce slightly for a few minutes.
Add the fresh lemon juice and drained capers, then simmer until the sauce reduces and thickens slightly, about 3–5 minutes.
Stir in the butter until melted, then return the chicken and any accumulated juices to the pan. Simmer over medium-low heat until the chicken is warmed through and the sauce reaches the desired thickness, about 2–3 minutes.
Remove the pan from heat and gently stir in the Greek yogurt if using, tasting and adding more if desired.
Serve the chicken alone or over cooked angel hair pasta, garnish with lemon slices and parsley, and enjoy.