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Melt butter in a large dutch oven or pot over medium-high heat.
Add the onion and cook for 3-4 minutes or until softened and light gold.
Add the garlic and sauté for another minute.
Add flour and whisk for 1-2 minutes or 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 medium-low and simmer for 15 minutes or until the broccoli and carrots are cooked through.
Stir in half & half and cheddar cheese and simmer for another minute.
Taste and adjust seasoning if needed.
Serve with toasted crusty bread or in a bread bowl if desired.