Preheat oven to 425 degrees F.
Trim stems from broccoli and toss in a bowl with olive oil salt and pepper. Spread out on a baking sheet.
Lay 6 slices of bacon onto a second baking sheet.
If both pans will fit in your oven, you can cook at the same time! Place in oven and cook for 15-20 minutes. Until the broccoli is nicely browned and the bacon is browned and crispy.
Remove from oven. Set broccoli aside until ready to use. Place bacon slices on a paper towel-lined plate to drain grease.
Place two slices of bread on a plate or cutting board. Top with 1 slices of cheese (or 1/4 cup of shredded), 3 slices of bacon, broken in half, half of the broccoli, then another slice of cheese. Top with the remaining 2 slices of bread.
Heat butter in a large skillet or griddle over medium heat. Place sandwiches in the heated skillet and cook for a few minutes, until golden brown and bottom layer of cheese is melty. Gently flip over with a spatula and repeat on the other side. Be sure not to have your heat too high, or it will burn the bread and the cheese won't be melted. Low and slow is the way to go, here.
Remove to plates, slice in half (I prefer a diagonal cut) and enjoy!