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1
Cut the broccoli into florets. Peel the stalks and cut them up too.
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2
Put the broccoli and the stock in a medium sized pot over medium heat. Cover and cook until the broccoli is very tender. This will take 10-15 minutes. Do not undercook the broccoli or your soup will not be smooth.
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3
While the broccoli is cooking, melt the butter in a small pot over medium heat. When it starts to bubble add the garlic, and stir for about 15 seconds until the garlic is fragrant. Do not let the butter or the garlic brown.
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4
When the butter is bubbly again, add the flour and stir with a wooden spoon until the flour is well incorporated and the mixture is beginning to froth.
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5
Take the mixture off the heat and add the milk. Whisk briskly and return the pot to the burner. Add salt, and cook, stirring quite frequently until the mixture thickens. If you notice the bottom starting to color, reduce the heat.
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6
Once the mixture has thickened, add the cheese and stir until it is incorporated.
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7
By this time the broccoli should be cooked. Take it off the heat.
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8
Use a hand blender to puree the broccoli mixture. (Or put it in a regular blender).
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9
Add the cheese sauce and blend.
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10
Season with salt and pepper to taste.
