Step 1Add the green beans to boiling, salted water and cook until tender, 6 to 8 minutes. Drain the beans, reserving the liquid. Add milk to the liquid to make 1 1/4 cups. Set the liquid aside.
Step 2Cook the onions in boiling salted water until they're tender, 20 minutes. Drain.
Step 3Melt the butter, add the flour and stir until smooth. Add the reserved green bean liquid. Cook until the sauce has thickened, stirring occasionally, 1 to 2 minutes. Season with salt and pepper to taste. Stir in the green beans and onions.