Step 1

Melt the butter in a large pot over medium heat, and mix in the flour. Reduce heat to low, and cook, stirring constantly, about 2 minutes. Mix in the chicken stock and milk, and season with salt and white pepper. Bring to a boil, reduce heat to low, and simmer about 10 minutes.

Step 2

Bring a pot of lightly salted water to a boil. Place the broccoli in the boiling water, and cook 2 minutes, or until just tender. Remove from heat, drain, and set aside.

Step 3

Gradually mix the processed cheese and Cheddar cheese into the large pot until melted. Mix in the broccoli. Continue cooking about 5 minutes.