Lightly season the chicken cutlets with salt and black pepper on both sides, then dust them evenly with 2 tablespoons of flour.
Warm a large skillet over medium-high heat and add vegetable oil. Lay the chicken cutlets in the pan without crowding them and cook each side until they develop a gentle golden sear.
Remove the chicken once it cooks through to an internal temperature of 165℉, taking care not to overcook.
Turn the heat to medium and melt the butter in the same skillet, then add the smashed garlic and cook until fragrant.
Whisk in 2 tablespoons of flour, then gradually pour in the half and half along with the chicken broth, stirring constantly to avoid lumps and bring the mixture to a boil.
After the sauce thickens, fold in the fresh spinach until it wilts and blends smoothly.
Return the chicken to the pan, coating each piece thoroughly with the creamy spinach sauce, then take the skillet off the heat promptly to keep the chicken tender.
Dish up the creamy spinach chicken and serve immediately for a cozy, satisfying meal.