Flatten the Chicken - Thoroughly dry the chicken breasts with a paper towel. Cut each piece horizontally lengthwise to make two thinner cutlets, four total. Place one of the pieces between two plastic sheets or a large plastic bag and flatten to an even ½-inch thickness. Repeat with remaining pieces.
Coat the Surface - In a medium bowl, combine flour, 1 teaspoon salt, and ½ teaspoon pepper. Lightly season each side of the chicken breast with salt and pepper. Dredge the pieces in the seasoned flour, shaking off any excess. Transfer to a plate and set aside.
Pan-fry the Chicken - Heat a large skillet over medium heat. Add the olive oil. Once hot, carefully add the chicken to the pan. Cook until both sides are golden brown, about 4 to 6 minutes per side. The internal temperature should reach 160 to 165ºF (71 to 74ºC). Transfer to a clean plate, loosely tent with foil to keep warm.
Make the Sauce - Using the same pan to cook the chicken, melt the butter over medium heat. Saute the shallots and garlic until fragrant, about 30 seconds. Add the wine, scraping the pan to remove any browned bits. Cook until almost evaporated, with a few tablespoons of wine remaining, about 3 to 4 minutes.
Reduce the Sauce - Stir in the heavy cream and chicken stock. Bring to a simmer over medium heat. Frequently scrape the pan's sides and bottom to ensure the cream does not curdle. Reduce the sauce until it starts thickening and lightly coats the back of a spoon, about 5 to 6 minutes.
Cook the Spinach - Stir in the spinach, and cook until wilted, about 1 minute.
Finish the Sauce - Turn off the heat and stir in the parmesan cheese, lemon zest, lemon juice, and nutmeg—season with salt and pepper to taste.
Warm the Chicken - Add the pieces back to the pan, coating with the sauce to reheat.
Plate & Serve - Garnish with some chopped parsley and serve hot.
Notes
Storing: Store in an airtight container for up to 5 days.
Reheating: Cover and microwave on the high setting in 15 to 30-second increments until hot.
Make it Gluten-Free: Substitute gluten-free flour, cornstarch, or skip the coating step.
Make it Keto: Coat chicken with almond or coconut flour, or skip the coating.
Using Frozen Spinach: Defrost 4 ounces of frozen chopped spinach, about 1/2 cup, and drain well.
Substituting for Wine: Use ½ cup of chicken stock, broth, or water instead of the wine to glaze the pan. You can add 1 teaspoon lemon juice or white wine vinegar to add some acidity to the liquid.