Melt butter in a large Dutch oven over medium heat. Add the onion and cook until softened and light gold. Add the garlic and sauté for another minute.
Add flour and whisk until the flour begins to turn golden in color. Pour in the chicken stock, broccoli florets, carrots, and seasoning. Bring to a boil then reduce heat to low and simmer for about 20 minutes until the broccoli and carrots are cooked through.
Stir in heavy cream and cheddar cheese and simmer for another 5 minutes.