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1. In a large pot, melt the butter over medium heat.
2. Add the flour and whisk to blend.
3. Reduce the heat to low and cook for 2 minutes, constantly stirring.
4. Add the stock and milk, salt and pepper and stir to combine.
5. Bring the mixture to a boil.
6. Reduce the heat to low and cook for 10 minutes.
7. Bring a saucepot of slightly salted water to a boil.
8. Add the broccoli and cook until tender, which takes about 2 minutes.
9. Remove the pot from the heat.
10. Drain and set aside.
11. Add the cheese to the pot and stir until melted.
12. Mix in the broccoli and cook for an additional 5 minutes or until hot.
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