Preheat the oven to 375˚F. Place green garlic in a small shallow baking dish and drizzle lightly with olive oil. Cover with aluminum foil, and roast until golden brown, 35-45 minutes. If the dish starts to burn before the garlic is roasted, add a tablespoon of water. Transfer to a wire rack to cool.
Bring a large pot of salted water to a boil. Add the pasta and cook according to package instructions. Drain, reserving 1/2 cup of the cooking water.
While the pasta is cooking, heat olive oil in a large skillet over medium-high heat. Add the pancetta and crushed red pepper, and sauté until pancetta is crisp and golden, about 5 minutes.
Peel and discard the outer layer of the roasted green garlic. Chop green garlic, then add it to the skillet of pancetta. Stir in the lemon juice and a generous pinch of salt and black pepper. Sauté for 2 minutes. Lower the heat, then add the pasta and arugula to the skillet. Toss gently until arugula wilts. Add a little of the reserved cooking water, a tablespoon at a time, so that you can scrape up any brown bits from the bottom of the pan. Taste and adjust the seasoning if needed, and served topped with grated Parmesan.