I wanted this soup to be a cross between a chicken pot pie and chicken soup and I believe this recipe hits the mark.
Put 1/2 inch of water in a large pan over medium heat; bring to a simmer, about 2 minutes. Place chicken in the simmering water, cover, and cook until no longer pink in the center and the juices run clear, 15 to 20 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Transfer chicken to a plate and shred when cool enough to handle.
Melt butter in a large pot. Add flour and stir continuously with a wooden spoon or whisk until a thick paste forms; continue cooking roux for 2 minutes. Add evaporated milk; stir until incorporated. Add chicken broth and stir until no lumps remain. Bring to a boil.
Add potatoes, carrots, chicken bouillon, pepper, and salt; cook until vegetables are tender, about 20 minutes.
Add shredded chicken and frozen peas and corn. Cook until heated through, about 5 more minutes.
Per Serving: 371 calories; protein 19.9g; carbohydrates 43.9g; fat 13.2g; cholesterol 67mg; sodium 1404.5mg.