Shred about two cups of breast meat from the rotisserie chicken and place in a large bowl. You can use two forks or your hands (my personal preference).
Pour 2/3 cup of bottled buffalo sauce over the shredded chicken and stir to combine. Set aside.
Chop 1/2 a medium yellow onion.
Heat 1 tbsp olive oil over medium-high heat in a large skillet.
Add the chopped onion and cook until soft and translucent, about 3-4 minutes. If the onion starts to brown too quickly, reduce the temperature to medium heat.
While the onions are cooking measure out two cups of low sodium chicken broth.
Make your roux. Melt butter in the same pan with the onions.
When the butter is melted, sprinkle the flour over the butter and onions, whisking constantly. NOTE: It is very easy to burn the flour, so be sure to keep whisking and lower the temperature if necessary.
Once the flour and butter are thoroughly combined, pour the chicken broth in in a steady stream. Whisk the mixture together until thickened, 3-4 minutes.
Add the tortellini and cook at a vigorous simmer according to the package directions, usually 4 minutes.
As the tortellini comes to the end of the cooking time, stir in the chicken tossed with buffalo sauce.
Top with the shredded cheese and stir to combine. Be sure to toss up from the bottom so everything is evenly covered in sauce.
Cook over medium heat until the cheese is melted and the chicken heated through, about 3-4 minutes.