Preheat the oven to 400oF. Spread the hazelnuts on a baking sheet and toast until lightly golden and fragrant, about 10 minutes.
Place the toasted nuts on a clean dish towel and rub them against one another until they lose most of their skins. Roughly chop the hazelnuts, place them in a bowl, and toss with a generous drizzle of oil. Season with salt and pepper and set aside.
In a medium bowl, mix together the parsley, olives, lemon juice, zest, and 1⁄2 cup oil. Set aside.
Bring a large pot of heavily salted water to a boil over medium heat. Add the pasta and cook according to package directions until al dente. Drain, reserving 1⁄2 cup of the pasta water.
Mince the garlic and anchovy together until they form almost a paste on your cutting board. In a large skillet, heat the 2 tablespoons oil over medium-high heat until it shimmers. Add the garlic-anchovy paste. Cook, stirring constantly, until the garlic is soft and fragrant, about 1 minute. Reduce the heat to low.
Pour the drained pasta into the skillet. Add the grated cheese and reserved pasta water and toss until the cheese is evenly distributed. Stir in the parsley and olive mixture and toss until the pasta is evenly coated.
Taste and adjust for seasoning and serve topped with toasted hazelnuts, habaneros, shaved cheese, and a sprinkle of Aleppo pepper.