Preheat your oven to 400°F (200°C). In a bowl, toss the chopped broccoli florets with olive oil, salt, and black pepper until they are well coated. Spread the broccoli evenly on a sheet pan and roast for about 15-20 minutes, or until the edges are crispy and the florets are tender. Stir halfway through roasting to ensure even cooking.
While the broccoli is roasting, take your slices of bread and butter one side of each slice generously. This will help achieve that golden, crispy exterior once grilled.
Once the broccoli is done roasting, it's time to assemble your grilled cheese. On the unbuttered side of one slice of bread, add a generous handful of shredded cheddar cheese, followed by a layer of roasted broccoli. Top it off with another slice of cheddar cheese before placing another slice of bread on top, buttered side facing out.
In a skillet over medium heat, place the assembled sandwich. Grill for about 3-4 minutes on one side, or until it is golden brown. Carefully flip the sandwich and grill the other side for another 3-4 minutes until the cheese is melted and both sides are perfectly crispy.
Remove the sandwich from the skillet and let it cool for a minute. Slice it in half and watch the melty cheese stretch as you pull it apart. Pair with your favorite soup for a delightful meal.