Melt butter in large saucepan. Sautee onions, carrots, celery, and potatoes until tender. Add flour, cook 1 minute. Add chicken broth, half and half or milk, and simmer over low hea, stirring constantly, until thickened. Remove from heat, add chicken and green beans, stir. Pour chicken and vegetable mixture into a 13"x9" baking dish. Set aside.
Prepare bisquits. Mix Bisquick and cheddar in a large bowl. Add milk, stir until a soft dough ball forms. Remove dough from bowl, place on a lightly floured suface. Rull dough to 1/2 inch thickness, cut into 2 1/2" rounds. Place rounds on chicken mixture in rows. Place any left over biscuits into a seperate pan.
Bake at 425 degrees for 30 minutes or until biscuits are browned and chicken mixture is bubbly. Remove from oven, brush biscuits with mixture of melted butter and garlic powder, also brush left over bisquits.