Add the spinach to the skillet. If using fresh spinach, stir it into the hot sauce until just wilted. If using thawed frozen spinach, make sure you’ve squeezed out as much liquid as you can, then stir it into the sauce until evenly distributed.
Pour the creamy spinach mixture evenly over the chicken in the baking dish, making sure each piece is nestled in the sauce. Sprinkle the shredded mozzarella over the top, then finish with the 2 tablespoons of grated Parmesan.
Bake, uncovered, for 20–25 minutes, or until the chicken is cooked through (internal temperature reaches 165°F/74°C) and the sauce is bubbling around the edges. If you like a deeper golden top, you can place the dish under the broiler for 2–3 minutes at the end—just watch it closely.
Remove from the oven and let the casserole rest for about 5 minutes. This gives the sauce a chance to settle and thicken a bit. Sprinkle with chopped fresh parsley if you like, then serve warm, making sure everyone gets a good scoop of chicken, spinach, and plenty of that cheesy sauce.