Begin by placing the chicken cutlets between two pieces of plastic wrap or parchment paper. Using a meat mallet, pound the chicken to about 1/2 inch thickness. Season both sides with salt and pepper.
Spread the all-purpose flour on a plate. Lightly coat each chicken cutlet in the flour, shaking off any excess.
In a large skillet, heat 1-2 tablespoons of olive oil over medium-high heat. Once hot, add the chicken cutlets in a single layer. Sauté for about 3-4 minutes on each side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the minced garlic and sauté for about 30 seconds until fragrant. Pour in the chicken broth and scrape up any browned bits from the bottom of the pan. Add the fresh lemon juice and capers, stirring to combine. Let the sauce simmer for about 5 minutes.
Stir in the unsalted butter and Greek yogurt until well combined and creamy. Return the chicken to the skillet, spooning the sauce over the top. Cook for an additional 2 minutes to heat through.
If desired, cook the angel hair pasta according to package instructions. Serve the chicken piccata over the pasta or on its own, garnished with sliced lemons and chopped parsley.