Cook the tortellini pasta according to package directions in a large pot of salted, boiling water. Reserve ½ to 1 cup of the pasta water, then drain well.
Melt the butter in a large pan over medium-high heat. Add garlic and cook for 30 seconds while stirring until fragrant. Add heavy cream, stirring to combine. Reduce heat to medium and season with salt, pepper, and cayenne pepper. Bring the sauce to a simmer for 3-5 minutes until thickened slightly.
Reduce the heat to medium-low, then whisk or stir in 1 cup of the Parmesan cheese until melted.
Add the cooked tortellini to the alfredo sauce and toss to coat evenly. If the sauce thickens up too much, add the pasta water, a little at a time, to thin it out. Sprinkle with chopped parsley and and the remaining Parmesan cheese. Serve with the cooked chicken on top or stirred in with the tortellini, if desired.