1) Preheat oven to 350 degrees Fahrenheit. Chop broccoli into big florets, drizzle with olive oil and sprinkle lightly with kosher salt and pepper. Bake broccoli for 20 minutes, stirring ever 8-10 minutes.
2) In a medium pot, melt butter over medium heat. Then add onions and peppers and cook until onions are soft, about 5 minutes.
3) Whisk in flour into the onions to form a light roux. Cook for a minute or two to cook out flour taste.
4) Whisk in warm milk slowly. The mixture should thicken into a nice cream sauce.
5) Add grated cheese and stir until melted. Reduce heat to low and keep warm.
6) When broccoli is done roasting, cut into very small florets. Then fold broccoli into the cheese sauce.
7) Season queso with salt and pepper.
Serve queso immediately with crusty bread or tortilla chips.