In a large pot of salted boiling water, cook the pasta until just al dente. Drain, reserving 1/2 cup of the cooking water.
Meanwhile, in a large, deep skillet, cook the pancetta in the oil over moderate heat until browned and crisp, about 10 minutes. Remove from the heat and stir in the shallot, parsley, chives, thyme and crushed red pepper.
Add the pasta and the reserved cooking water to the skillet and toss over low heat, scraping to remove any bits stuck to the bottom of the pan, until almost all of the water has been absorbed, about 1 minute. Stir in the arugula and transfer the spaghetti to a wide, shallow serving bowl. Toss with the grated cheese and season with salt and pepper.
In a medium skillet, cook the butter over moderate heat, stirring, until golden brown and nutty smelling, about 5 minutes. Crack the eggs into the pan and cook until the whites are just set and the yolks are runny, about 3 minutes. Season with salt and pepper. Slide the eggs into the pasta and toss, breaking up the eggs to distribute them evenly. Serve hot.