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Melt butter in a large Dutch oven over medium heat. Add onions and garlic, stir and sauté until soft – 3 to 4 minutes. Sprinkle in all-purpose flour and whisk continuously for 1-2 minutes.
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Whisk in the chicken stock, milk, and cream. Bring to a boil then reduce heat to medium-low.
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Add the broccoli and carrots. Cook for 20-25 minutes or until the broccoli is tender.
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Remove one cup of soup and puree with an immersion blender (optional for smoother soup). Return pureed soup to the pot. For a chunkier soup, skip this step.
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Reduce heat to low and stir in the shredded cheddar cheese, one handful at a time. Stir in nutmeg, salt and pepper.
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Serve with crusty bread or in a bread bowl.