In a skillet, melt 1 tablespoon butter over medium heat. Sauté onions till translucent and set aside.
In a bowl, whisk together ¼ cup butter and flour and heat over medium heat in a large saucepan. Add 1 or two tablespoons of milk if necessary to keep the flour from burning. Stir continuously for about 3-4 minutes.
Stir in the chicken stock and bring to a simmer. Add the veggies and cook until tender. Stir in the cheese and mix until the cheese melts. Season and serve hot.