Preheat the oven on to 200 F. 

In a shallow dish, combine the flour, ½ tablespoon salt and ½ teaspoon pepper, stirring until mixed well.  Thoroughly coat the chicken cutlets with the remaining salt and pepper. Dredge the chicken cutlets on both sides in the flour mixture, shaking off the excess. Set aside.

In a frying pan over medium high heat, heat 2 tablespoons of the room temp butter and 2 tablespoons of the olive oil, stirring until the butter is melted, combined with the olive oil and bubbly. Place 2 of the chicken cutlets into the pan and sauté for 3 minutes. Flip and sauté the other side for 3 minutes.  If the flour starts to burn before the cutlets are done cooking, reduce the heat. (For thicker chicken cutlets, reduce heat slightly, cover and cook for an additional 1 minute, or until the cutlet is cooked thoroughly.) Transfer the cutlets to a baking sheet and place in the oven to keep warm. 

Using a paper towel, wipe the pan clean. Return the pan to the stove over medium heat and add 2 Tablespoons of butter and 2 Tablespoons olive oil, repeating the cooking instructions for the remaining two chicken cutlets. 

When done sautéing the chicken, use a paper towel to wipe the pan and return to the stove over medium heat. Add the wine to the pan and cook for 1 minute. Add the lemon juice, cooking for 30 more second. Add the cold butter and the capers, stirring and cooking for 1 minute.

Reserving a little of the sauce in the pan, pour the sauce into a bowl and set aside. Return the pan to the stove and place the spinach in the pan, stirring or 1 minute, or until wilted.

Serve the chicken with the spinach, topped with sauce and garnished with lemon wedges on the side.