Preheat the oven to 400°F (200°C).
On a sheet pan, toss the broccoli florets (from 1 medium head, about ½ pound, chopped small) with 2 tablespoons olive oil, 1/2 teaspoon salt, and 1/4 teaspoon freshly cracked black pepper. Spread in a single layer.
Roast the broccoli 8 to 10 minutes, until evenly roasted but not burnt. Remove from the oven and let cool until cool enough to handle.
Heat a skillet over medium-low heat.
Spread softened unsalted butter evenly on one side of each of the 6 to 8 slices of bread.
Assemble sandwiches: place half the bread slices buttered side down (unbuttered side up). Divide the 1 cup cheddar cheese evenly among them, placing some cheese on each unbuttered slice. Divide the roasted broccoli evenly over the cheese, then add more cheese on top of the broccoli so the broccoli is between two layers of cheese. Top each with the remaining bread slices, butter side out.
Cook the sandwiches in the preheated skillet, working in batches if needed. "Grill" until the bread is golden brown and the cheese melts, turning each sandwich over once. Cook over medium-low heat to prevent burning (about 3–4 minutes per side, adjusting as needed).
Remove from the skillet, let the sandwiches rest 1–2 minutes, then slice and serve.
If you prefer, use gluten-free bread in the same way.