Cut the chicken breasts into three or four slices each on the bias, against the grain. Use a meat mallet to pound to an even ½-inch thickness. Season the chicken with ½ teaspoon salt. Spread the flour on a plate or shallow bowl.

Heat a large skillet over medium heat, and add 2 tablespoons of the butter and the olive oil. Lightly dredge the chicken in the flour, and add as many pieces to the skillet as will fit in one layer without crowding. Brown the chicken in batches, removing the slices to a plate as they brown, about 3 minutes per batch.

Once all of the chicken is out of the pan, add the sliced garlic, and cook until it’s sizzling, about 1 minute.

Scatter in the spinach, and season with ½ teaspoon salt and a pinch of peperoncino. Toss to coat the spinach in the oil. Cover, and cook until it’s wilted, 3 to 4 minutes. Remove the spinach to a serving platter, letting the juices drip back into the pan.

Increase the heat to medium high, and add the remaining 2 tablespoons butter to the skillet. When it’s melted, add the lemon slices, and cook, turning once, until browned on the edges, about 1 minute. Add the capers. Let them sizzle a minute; then add the white wine and lemon juice. Simmer rapidly to reduce by half. Add the stock, and simmer rapidly until the liquid is slightly thickened and saucy, 1 to 2 minutes. Slide the chicken back into the pan, and heat it through, 1 to 2 minutes. Sprinkle with the parsley, and toss. Serve the chicken and sauce on top of the spinach.