Add the chicken, carrots, onion, frozen mixed vegetables, chicken stock, stock cube, salt, and black pepper to a large soup pot. Stir to combine.
Bring the soup to a gentle simmer over medium heat. Reduce the heat as needed and cook for 30 to 40 minutes, or until the vegetables are very tender and the chicken is fully cooked.
Remove the cooked chicken from the pot and transfer it to a plate. Shred the chicken into bite-sized pieces using two forks and set aside.
Carefully blend the vegetables and broth with an immersion blender until smooth and creamy. If using a countertop blender, work in batches and take care when blending the hot soup.
Return the shredded chicken to the pot and stir until evenly distributed throughout the soup.
Add the butter and stir until completely melted and combined. Taste and adjust the salt and black pepper as needed.