Steam or cook carrots and green beans in boiling water. Cook until tender, about 12 minutes. Remove from heat with them still firm and drain.
Melt butter over medium heat. Saute onions and mushrooms until almost tender, about 5 minutes.
Reduce heat, cover, and simmer for 3 minutes.
Stir in green beans, carrots, salt, garlic, and pepper. Cover and cook five minutes on med/low heat.