Preheat oven to 400 degrees. Line a baking pan with parchment paper.Place potatoes in a bowl and toss with olive oil and sprinkle with a pinch of salt and pepper.Place potatoes on parchment paper – cut side down and bake for 30 minutes (until golden brown and tender). Leave oven on if serving right away.Place broccoli in a steamer over boiling water and steam until just tender, about 3 minutes (or blanched in salted water for 2 minutes.) If cooking the broccoli ahead of time, remove from the pot and immediately refresh under cold water to stop the cooking process.Top each potato with a pinch of cheese and then a broccoli floret and bake until cheese is melted or broil it for a few minutes to speed things up.Sprinkle each with a pinch of grated cheese, if desired.