Preheat your oven to 400°F (200°C).
In a mixing bowl, combine the chopped broccolini, olive oil, salt, and black pepper. Toss until well coated.
Spread the seasoned broccolini on a baking sheet and roast for about 15-20 minutes, stirring halfway through.
While the broccolini is roasting, butter one side of each slice of bread. Layer cheese and roasted broccolini on the unbuttered side, then top with more cheese and another slice of bread, buttered side out.
Heat a skillet over medium heat and cook the sandwiches for about 3-4 minutes on each side until golden brown and crispy.
Remove from the skillet, let cool for a minute, slice in half, and serve warm.
