Melt butter in a large pot over medium heat. Add garlic and onion; cook and stir until the onion has softened and turned translucent, about 5 minutes. Stir in the flour, thyme, and pepper until blended.
Pour in the chicken broth and bring to a simmer. Add the chicken cubes and mushrooms; cook until the chicken is no longer pink in the center, about 10 minutes.
Stir in the cream of mushroom soup; simmer for 5 minutes more.