Start by slicing the chicken breasts lengthwise to create four thinner cutlets. Trim off any visible fat.
Season the chicken with salt, pepper, and garlic powder, then coat each piece lightly in flour.
In a skillet over medium-high heat, add 2 tablespoons of the butter along with the olive oil.
Once hot, add the chicken cutlets and cook for 4-5 minutes on each side until golden brown. Transfer to a plate and set aside.
Remove the skillet from heat and carefully add in the chicken broth, lemon juice, lemon zest, remaining butter, and drained capers.
Scrape up the browned bits stuck to the pan for added flavor.
Stir in the heavy cream and return the skillet to heat, allowing it to bubble gently.
Add the chicken back into the pan to coat with the sauce and cook for another 5 minutes or until fully cooked.
If the sauce becomes too thick, add more broth to loosen it up.
Garnish with chopped parsley and freshly grated parmesan cheese if desired.
Serve warm and enjoy your meal.