If not already, cut or pound the 2 pounds chicken breast into thin cutlets. Pat dry if needed.
In a shallow dish, combine 1/3 cup flour, 2 teaspoons garlic powder, 1/2 teaspoon salt, and 1/2 teaspoon pepper.
Dredge each chicken cutlet in the flour mixture, coating both sides lightly; shake off excess flour.
Heat 1 tablespoon olive oil in a large heavy skillet over medium heat until hot.
Working in batches so you do not overcrowd the pan, lay cutlets flat in the skillet. Cook 3–4 minutes on the first side without flipping, then flip and cook about 3 minutes on the other side, until golden and almost cooked through. Transfer cooked cutlets to a plate and repeat with remaining chicken.
Reduce heat to low. Add 5 tablespoons butter to the pan and stir, scraping any browned flour and chicken bits from the bottom. Cook about 1 minute, until the butter and bits are lightly golden.
Add 1/2 cup chicken broth and 1/3 cup fresh lemon juice to the pan, stirring and scraping the browned bits until the sauce is smooth. Increase heat to bring the sauce to a simmer.
Slowly stir in 1/2 cup heavy cream, then add 1/4 cup brined capers (drained); stir to combine.
Keep the sauce at a gentle simmer and cook until it thickens slightly, about 2–3 minutes.
Return the chicken to the skillet, spoon sauce over the cutlets, and simmer 4–8 minutes more, until chicken is cooked through (165° internal temperature). Remove from heat and serve.