Preheat oven to 450 degrees F. Cut florets off of broccoli stalks and spread out on a baking sheet with sliced Fresno peppers and garlic. Drizzle with olive oil and season with salt and pepper.
Roast veggies until they are charred on the edges, about 15 minutes.
After veggies roast, roughly chop them and stir together with cheddar cheese. I prefer to cube my cheese into small cubes, but you could also grate it.
Heat a sturdy skillet over medium heat and lightly butter your bread slices. Place the slices butter-side down on the skillet and pile on some of the broccoli mixture.
Cover with a second piece of bread, butter-side up. Cook the sandwich until the bread is toasted and the cheese is very melted, about 5 minutes per side. Keep a close eye on the sandwiches to avoid burning the bread. Flip the sandwich if it is cooking too quickly.
Serve sandwiches while warm and chop in half for easier eating.