Heat a large pot of water for pasta, 5-6 quarts.
Heat a large nonstick skillet over medium-high heat with about 3 tablespoons EVOO, 3 turns of the pan. Add pancetta and render about 3 minutes, add corn and its liquids and stir a minute, then add garlic, stir, add crab, lemon zest, scallion whites, thyme and chili pepper, paste or flakes, then stir a minute or 2 more. Add dry vermouth or wine and let it absorb.
Salt water and drop pasta and cook 1 minute less than package directions for al dente. Reserve 1 full cup cooking water just before draining.
Whisk egg yolks and cheeses, then add 1 cup cooking water to temper eggs.
Remove the crab and corn from heat, douse with juice of lemon, toss with pasta and the egg sauce, then add scallion greens and the parsley. Serve immediately with extra grated cheese to pass.