Step 1: Preheat the oven to 400°F (200°C).
Step 2: In a mixing bowl, combine the chopped broccoli, olive oil, salt, and black pepper. Toss until well coated.
Step 3: Spread the seasoned broccoli onto a baking sheet in an even layer. Roast for 15-20 minutes, stirring halfway through.
Step 4: Butter one side of a slice of bread, place it buttered side down, layer with cheese and broccoli, then top with another slice of bread.
Step 5: Heat a skillet over medium heat. Grill the sandwich for 3-4 minutes on each side until golden brown and cheese is melted.
Step 6: Remove from skillet, let cool for a minute, then cut in half and serve warm.