Pat the chicken cutlets dry with paper towels.
Season both sides with half of the oregano, salt, and black pepper.
Coat each cutlet lightly in flour and shake off the excess.
Heat 2 tablespoons olive oil in a large skillet over medium-high heat.
Cook the chicken for about 3 minutes per side until lightly golden. Remove to a plate.
Add a little more olive oil if needed.
Add the sliced mushrooms and cook for about 1 minute.
Stir in the tomatoes, garlic, remaining oregano, salt, pepper, and 2 teaspoons flour.
Cook for 3 minutes while stirring frequently.
Pour in the chicken broth, then add the lemon juice and remaining chicken broth.
Bring the sauce to a gentle boil.
Return the chicken to the skillet and spoon some sauce over the top.
Cook for 3 minutes over medium-high heat.
Reduce heat to medium-low, cover, and cook for another 7–8 minutes until the Italian Skillet Chicken reaches an internal temperature of 165°F (74°C).
Stir in baby spinach just before serving, if desired.
Serve hot with orzo, pasta, rice, mashed potatoes, or warm Italian bread.