In a small frying pan, heat up a touch of oil over medium heat. Cook the broccoli until bright green and tender, stirring occasionally. Season with salt and pepper.
When your broccoli is done cooking, heat up a non-stick pan on medium-low heat. Butter one slice of bread and place in the pan butter-side down. Top with half of the shredded cheddar and the broccoli. Add the remaining cheddar on top of the broccoli, making sure to get to the edges. Butter the other slice of bread and place on top of the cheese, butter-side facing out. Cook slowly on medium-low heat until golden brown and toasty. Most of your cheese should be melted when it’s time to flip. Carefully flip your sandwich and continue grilling. The second-side grills a bit faster, so turn the heat down to low and keep a close eye on it. When perfect, remove from the pan, and enjoy hot!