In a large stockpot, combine the chicken breasts, chopped bell peppers, and onions. Add enough water to cover the ingredients and bring to a boil over medium-high heat. Reduce the heat and let it simmer until the chicken is cooked through, approximately 30 minutes.

Once the chicken is cooked, remove it from the pot and set it aside to cool. Strain the cooking liquid to remove the vegetables, reserving the broth. When the chicken is cool enough to handle, remove the skin and bones, then chop the meat into bite-sized pieces.

Return the reserved broth to the stockpot. Add the chopped chicken, chicken broth, red potatoes, frozen mixed vegetables, rotini pasta, and carrots. Season with salt and freshly ground black pepper. Bring the mixture to a boil over medium-high heat.

In a small bowl, whisk together the Wondra flour and water until smooth. Gradually stir this mixture into the boiling soup. Reduce the heat to medium and let the soup simmer until it thickens slightly, about 5 minutes.

Stir in the heavy cream and butter, allowing the butter to melt completely. Continue to simmer the soup for an additional 10 minutes, stirring occasionally, until it's heated through and well combined.