Heat oil and butter in a large dutch oven, over a medium heat. When butter is melted, add the chicken. Season with a third of the salt, pepper, and garlic salt. Cook until lightly browned, about 5 minutes, stirring frequently.
Sprinkle flour over the chicken and cook until combined, stirring constantly. Gradually stir in chicken broth. Begin with 3 cups and add more later if too thick.
Season the celery, carrots, onions, and potatoes with one third of the seasonings. Stir into the chicken broth, and bring to a low boil. Reduce to low simmer and cook. uncovered, about 25-30 minutes, stirring frequently. If broth is too thick, add remaining cup of broth.
Stir in the frozen peas and cannellini beans. Check seasonings and add remaining salt, pepper and garlic salt if needed. Simmer 10 minutes. Remove from heat.
May serve now, or allow to set for flavors to blend. Reheat over low heat. Serves 6