Bring a large pot of water to a boil and season with salt. Prepare a large bowl of ice water. Blanch the broccoli by throwing the florets into the boiling water for 30 seconds. With a slotted spoon, remove the florets to the ice water. When cool, drain and set aside. Keep cool in the fridge.
To make the sauce, melt the butter in a pot over medium heat. Add the green onions and cook for 2 minutes. Sprinkle in the flour, whisk to combine and cook until thickened, about 1 minute. Pour in the milk and heat until thickened, 4 to 5 minutes. Add the grated cheese, cream cheese, chili powder, cumin, 1/2 teaspoon salt and pepper to taste. Stir to melt. Taste and adjust the seasonings.
Serve hot as a dipping sauce with the cold broccoli.