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Step 1
Bring a large pot of salted water to a boil over high heat. Cook the pasta for 8 minutes (or just 2 minutes under the suggested cooking time). Drain well, reserving 1½ cups of pasta water.
Step 2
Meanwhile, heat a large straight sided skillet over medium heat. Add the olive oil and pancetta. Cook stirring often with a wooden spoon until the pancetta is crisp, about 10 minutes. Add the pepper and toast, stirring often, until fragrant. Add 1/2 cup of pasta water to the pan and scrape up all the bits that are sticking to the bottom.
Step 3
Add the pasta and sprinkle with the Parmesan cheese. Add another 1/2 cup pasta water and stir to coat all of the pasta in the cheese. Add the pecorino and the butter and stir to combine, creating a light creamy cheese sauce. Add the arugula and cook until wilted. Add additional pasta water as needed to maintain the light sauce consistency. Serve with more grated cheese if desired.