In a large skillet, melt 2 tablespoons of the unsalted butter over medium heat. Add the sun-dried tomatoes (along with 1 tablespoon of their oil) and sliced mushrooms. Cook for about 5-7 minutes, or until the mushrooms are tender. Stir in the minced garlic and cook for an additional minute until fragrant.
Sprinkle the flour over the sautéed vegetables and stir to combine. This will help thicken your sauce. Cook for about 1-2 minutes, then add the Italian seasoning, paprika, and red pepper flakes (if using). Gradually whisk in the whole milk and chicken broth until smooth. Bring the mixture to a gentle simmer, stirring frequently.
Once the sauce has thickened slightly, reduce the heat to low and stir in 1/2 cup of the grated Parmesan cheese. Mix until melted and incorporated, creating a creamy sauce that coats the back of a spoon.
Add the refrigerated Rana tortellini directly to the sauce. Cook according to package instructions, usually about 3-5 minutes, until the tortellini is al dente. Stir gently to ensure each piece is coated in the delicious sauce.
Once the tortellini is cooked, fold in the shredded rotisserie chicken and chopped spinach. Cook for an additional 2-3 minutes, until the spinach is wilted and everything is heated through.
Season with salt and pepper to taste. Sprinkle the remaining 3 tablespoons of Parmesan cheese on top before serving.