Lay chicken breasts on a plastic cutting board. Set a folded paper towel under each to prevent slipping while you cut the chicken into culets. Place a hand on top of one of the breasts and with a large, sharp knife, slowly slice lengthwise down the center of the chicken. About halfway through, the chicken may start to wiggle, at this point, you can peel the top half back with your hand and continue slicing all the way through. Do the same for the second breast.

Working two or four at a time, cover the chicken with parchment or plastic, and pound with a meat tenderizer, rolling pin, or small pan, until the chicken is about 1/4-inch thick. Sprinkle both sides of the chicken generously with sea salt and pepper.

Dump flour into a shallow bowl and dredge chicken on both sides, shaking any excess flour off.

Set a large cast iron skillet over medium-high heat. Add grapeseed oil and butter, and stir. Add two chicken cutlets and cook until a rich golden brown, 2 - 3 minutes per side. If pan starts to smoke, edge heat closer to medium. Keep cooked chicken warm on wire rack in a 200 degree F oven.

If you haven't already, turn heat down to medium. If pan is dry, add a drizzle of grapeseed oil. Add shallots. Cook, stirring often, until shallots are golden, 2 - 3 minutes. Add capers, lemons, and white wine. Edge heat up to medium-high, and cook until mixture starts to thicken, about 4 minutes. Add butter and stir; cook, stirring occasionally, until mixture thickens considerably, about 4 minutes more. Add sea salt to taste. Remove from heat and spoon sauce into a small bowl.

Arrange cutlets on a platter. Drizzle with the pan sauce. Finish with parsley. Serve with al dente angel hair noodles and asparagus or greens.