Heat 1 tablespoon of olive oil in a large 12-inch skillet over medium-high heat. Season both sides of the flattened chicken breasts with salt and pepper.

Place some flour in a shallow dish and dredge each chicken breast in the flour, making sure both sides are coated evenly. Shake off any extra flour.

Place the chicken breasts in the heated skillet. Cook for 4 to 5 minutes on each side, or until fully cooked (the internal temperature should reach 165°F). Once done, transfer the chicken to a plate.

Lower the heat to medium-low and return the skillet to the stove. Add the remaining tablespoon of olive oil. Sauté the shallot for about 1 minute, then add the garlic and cook for another 20 seconds.

Pour in the chicken broth and sprinkle in the Italian seasoning. Turn the heat up to medium-high and bring the mixture to a simmer.

Once it starts simmering, lower the heat to medium-low and let it cook until the liquid reduces by about two-thirds, which should take around 10 minutes.

In a small bowl, whisk together the cornstarch and 1 1/2 tablespoons of chicken broth. Slowly whisk this mixture into the reduced broth in the skillet. Add the spinach and cook, stirring occasionally, until the sauce thickens and the spinach wilts.

Stir in the cream and add the cheese, mixing until the cheese has melted and the sauce is smooth. Remove the skillet from the heat.

Return the chicken to the pan, coating it with the creamy spinach sauce. Spoon the sauce over the chicken and serve.