Preheat the oven to 400F and preheat a large ovenproof skillet to medium-high heat with the olive oil. When the skillet is very hot, add the butter to melt. When the butter has melted, add the brussels to the skillet in one even layer.
Let the brussels cook for 5 minutes, undisturbed. Toss the sprouts after 5 minutes, and sprinkle on the salt, crushed red pepper, and two tablespoons of the parmesan. Arrange the sprouts back into one even layer and transfer the entire skillet to the oven.
Roast the brussels sprouts for 7-10 minutes until bright green and just barely tender. Remove from the oven and toss once more, then sprinkle the skillet with the remaining tablespoon of grated parm. Serve immediately. Enjoy!