Bring a pot of salted water to a boil over medium-high heat, using less water than normal. (This helps to concentrate the starch in the pasta water, which is used to thicken the sauce in this recipe.)
Cook the spaghetti until al dente according to package directions, about 8-10 minutes. Do not drain.
In the last few minutes of cooking the pasta, add pepper to a nonstick skillet over medium heat. Cook for 20 seconds to 1 minute, stirring occasionally, until the pepper is fragrant. (Watch carefully, being careful not to burn the pepper.)
Add oil and about ½ cup of pasta water, stirring to combine. Using tongs, remove cooked spaghetti directly from the cooking water into the skillet. Stir to coat spaghetti with the olive oil and pepper. Cook for 2 more minutes, stirring frequently. (This allows more starch to cook out.)
Remove the skillet from heat, and allow the pan to cool for about 30 seconds. (If the noodles or the pan are too hot, the cheese could separate in the next step.)
Working in batches, add the cheese to the skillet. Stir continuously until the cheese is melted and has fully coated the spaghetti. Add more pasta water as needed, ¼ cup at a time, to achieve your desired consistency. If the cheese has separated, return the skillet to the heat until the cheese fully melts and evenly coats the pasta.
Garnish with pepper and Pecorino Romano cheese. Salt to taste. Serve immediately.