Preheat oven to 350 F. Peel and dice potatoes into 1-inch pieces. Place potatoes into a large saucepan. Cover with water. Bring potatoes to a boil over medium heat.
Let potatoes cook for about 15-20 minutes, or until fork tender. Drain and place potatoes into a large bowl. Cook broccoli according to package directions, drain. Add butter, salt and pepper to potatoes and mix with a hand mixer until smooth.
Fold in cooked broccoli florets and 1/2 cup shredded cheddar cheese into the mashed potatoes. Spread mixture out into a greased baking dish. Top with the remaining shredded cheddar cheese and breadcrumbs. Bake for 30 minutes.
