Preheat the oven to 350 degrees F. Grease a 9x13-inch baking dish with oil and set it aside.
Cook the frozen tortellini in salted water according to package instructions. Drain and set aside.
In a large skillet, melt butter over medium heat. Once melted, sprinkle in the flour and cook for a minute.
Add minced garlic and cook for a couple more minutes.
Stir in chicken broth and cook for 3 minutes.
Pour in the heavy cream, then add salt and pepper.
Stir in Parmesan cheese and let the sauce simmer for a couple of minutes until it thickens slightly.
Add the cooked tortellini, spinach, and chicken to the skillet, tossing until well combined.
Transfer the mixture to the prepared baking dish and top with a layer of mozzarella cheese.
Place in the oven and bake for 20-25 minutes, until the cheeses are melted and bubbly on the sides.
Once done, garnish the creamy tortellini with freshly chopped parsley before serving.