Melt butter in a large pot over medium- high heat. Whisk in flour and cook, stirring continuously for 2 minutes, or until golden brown.
Whisk in chicken broth and cook for 2-3 more minutes, or until thickened. Whisk in milk and mix until smooth. Add chicken bouillon cubes and mix until dissolved.
Add onion, mushrooms, frozen vegetables and potatoes; mix until combined. Bring to a boil, then reduce heat to low and let simmer for 20 minutes or until vegetables are tender.
Add chicken and season with salt and pepper, and cook for a few additional minutes until chicken is heated through.