In a 3-quart saucepan, melt butter or margarine. Add onion and green onions. Cover and cook over medium-low heat for 15 minutes, stirring occasionally, until onions are very tender.
Stir in the flour, salt, and pepper. Add milk and chicken broth. Cook and stir until thickened and bubbly. Cook and stir for 1 minute more.
Add half-and-half. Cook and stir until heated through. Serve topped with croutons, if you like. Makes 6 side-dish servings.