Butter
Chicken stock
All-purpose flour
Half-and-half
Broccoli florets
Carrots
Dijon mustard
Cheddar cheese
Onion
Garlic
In a small saucepan, add 1 tablespoon butter, the diced onion, and sauté over medium heat until the onion is translucent and barely browned, about 4 minutes. Stir intermittently.
Add the garlic and cook about 30 seconds, stirring constantly so it won't burn. Remove from heat and then set the pan aside.
In a large heavy-bottom pot, add 4 tablespoons of butter and flour. Cook over medium heat for about 3 to 5 minutes, whisking constantly until flour is thickened.