Place the chicken in a medium saucepan and season it generously with salt and ground black pepper. Pour in enough water to cover the chicken by approximately 1 inch.
Bring the water to a boil over high heat. Once boiling, reduce the temperature to low, cover the saucepan, and simmer for 10–20 minutes, depending on the thickness of the chicken, until it is fully cooked.
Transfer the cooked chicken to a large mixing bowl or the bowl of a stand mixer. Shred it into bite-sized pieces using two forks, a hand mixer, or a stand mixer. Set the shredded chicken aside.
Add the olive oil and unsalted butter to a large soup pot or Dutch oven and warm over medium heat.
Once the butter has melted and the pot is hot, add the diced yellow onion with a small pinch of salt. Cook for approximately 3 minutes, stirring periodically, until the onion begins to soften and becomes translucent.
Stir in the chopped sun-dried tomatoes and minced garlic. Continue sautéing for another 3 minutes, stirring occasionally, to develop their flavor.
Sprinkle the Italian seasoning, crushed red pepper flakes, paprika, and ground black pepper into the pot. Stir briefly to distribute and lightly toast the seasonings.
Add the reserved shredded chicken, rinsed cannellini beans, fire-roasted diced tomatoes along with their juices, and chicken broth.
Mix thoroughly, then taste the broth and adjust the salt, black pepper, or other seasonings as necessary.
Increase the heat to medium-high and bring the soup to a boil. Cover the pot and allow the soup to cook for 10 minutes.
Check the cooking time listed on the tortellini package. When the remaining soup-cooking time equals the required pasta cooking time, add the gluten-free cheese tortellini directly to the boiling soup.
Cook according to the package directions until the tortellini are tender and rise to the surface. Check one piece for doneness before removing the soup from the heat.
Once the tortellini are fully cooked, turn off the heat.
Stir the chopped kale and grated Parmesan into the hot soup. Continue stirring until the kale softens and the Parmesan has melted into the broth.
Gradually pour in the heavy cream while stirring continuously to help keep the mixture smooth and prevent the cream from curdling.
Taste the finished soup and make any final seasoning adjustments. Additional grated Parmesan may be added immediately before serving for a richer finish.