Bring a large pot of water to boil. Season with salt and add the pasta and cook, stirring occasionally, until al dente. Reserve 3/4 cup of the pasta cooking water and then drain the rest. Place the pasta aside for a moment.

In a large skillet, add the butter and melt over medium heat. Add the shredded Brussels sprouts and sauté until golden, about 5 minutes. Add the cracked black pepper and stir to combine.

Add 1/2 cup of the reserved pasta water to skillet and bring to a simmer. Add the cooked pasta and reduce heat to low. Add the grated Parmesan and tossing with tongs until melted. Remove pan from heat and add the grated Pecorino, stirring and tossing until melted. If the pasta still looks a bit dry, add the remaining reserved water and toss to combine. Transfer pasta to a serving dish and serve immediately.