Lay a piece of plastic wrap over the meat on the cutting board.  Pound the breast thin with the smooth side of a meat mallet.  Start in the center and move outward, stopping when you have achieved your desired thickness.

Place the breasts on two plates, then sprinkle both sides with salt and pepper.

Heat the olive oil in a 10-inch skillet over medium high heat.  Once the oil starts shimmering, place the breasts in the skillet.  Turn the heat down to medium and cook it for 6 minutes per side, or until golden brown.  Turn down the heat to medium low if the oil starts spitting.  Put the cooked chicken on two clean plates.

Pour in the stock to deglaze the pan and scrape the bottom to loosen any browned bits.

Decrease the heat to medium and add the cream, Parmesan cheese, lemon juice, and capers.  Sprinkle in salt and pepper and bring to a gentle simmer.  Let it cook for a couple of minutes, whisking occasionally.

While the sauce is simmering, make the beurre manié by mixing equal parts softened butter and flour.  Add one small spoonful of the butter paste to the sauce at a time, whisking until it's incorporated.  Keep adding it a spoonful at a time until the sauce is thickened.  The beurre manié will add a nice shine and satiny texture to the sauce.