Preheat your oven to 400 degrees F (200 degrees C)
Roughly chop and break apart the Broccoli (1 head).
Place on a baking sheet with parchment paper with Olive Oil (1 tablespoon), Salt (to taste), and Ground Black Pepper (to taste). Bake until roasted throughout about 20-30 minutes. Set aside.
In the meantime, heat a cast iron with a small layer of olive oil.
Take your Sourdough Bread (4 slice) and spread on Mayonnaise (2 tablespoon) on both slices. This helps it toast evenly and crisp nicely.
Mayo side down, place on the cast iron. Add on your Extra Sharp White Cheddar Cheese (1/2 cup), Medium Cheddar Cheese (1/2 cup), and roasted broccoli. Top with the second piece of sourdough with mayo side up.
Once the bottom of the sourdough is toasty, gently flip, press down so it crisps and the grilled cheese stays together. Cook and melt through for another 5-6 minutes until the cheese has melted and both sides of your bread are toasty.
Remove from your cast iron, slice, and serve.