Preheat oven to 400 degrees.
Mix broccoli, olive oil, salt and pepper on cookie sheet until combined. Roast for 8 minutes, careful not to burn it. Remove from oven.
Heat a skillet over medium heat.
Spread butter on one side of each bread. The buttered sides will be the outside of the sandwich.
On the nonbuttered side of bread layer cheese, broccoli and more cheese. Top each with the other piece of bread, making it a sandwich.
Add to skillet and grill until the cheese is melted and bread is toasted, turning sandwiches over once while grilling.