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Bring a large pot of water to a boil. Season with a pinch of salt and add the spaghetti. Cook until al dente according to the package instructions. Before draining, reserve about 3/4 cup of the pasta cooking water.
While the pasta cooks, peel the garlic and thinly slice each clove.
Heat a large skillet over medium-low heat and add a generous glug of extra-virgin olive oil. Add the sliced garlic and a few grinds of freshly ground black pepper. Sauté for 2–3 minutes, or until the garlic is just starting to turn golden.
Drain the spaghetti, then add it directly to the skillet. Toss well to coat the pasta in the oil, garlic, and pepper.
Keep the skillet over low heat. Gradually sprinkle in the grated Pecorino Romano, adding a splash of the reserved pasta water as you stir vigorously until the sauce emulsifies and becomes very creamy.
If the sauce seems too thick, add more of the reserved pasta water, a little at a time, until you reach your desired consistency.
Serve immediately, topped with extra grated Pecorino Romano and more freshly ground black pepper to taste.