How to Make It
In a large saucepan over medium high heat, cook the bacon until it is rendered and browned. Remove to a plate with paper towels to drain. Blot the residual bacon fat out of the pan with a paper towel, but leave any crispy bits that might be stuck.
Add two cups of water, the butter, and 1/2 cup of the Parmesan cheese to the pot. Heat over medium-high heat, stirring constantly, until you have a creamy looking broth, being sure to scrape the bottom to get those bacon bits added to the mix. Add the two squares of noodles in to cook, stirring frequently, until they are softened. Keep stirring until the noodles are al dente and the sauce is thickened, about 3-4 minutes. Pour off the excess broth into a small bowl, leaving the noodles a bit soupy but not swimming. Essentially you want the broth to come up halfway of the depth of the noodles. You should have about 1/2 cup of reserved broth. Keep stirring until the sauce reduces a bit and just coats the noodles, maybe another minute.
Push the noodles to one side of the pan and add the eggs in the space you create, stirring them inside that hole until they begin to form large curds, then mixing the eggs in with the noodles. Add the bacon bits, and remaining cheese, and the reserved broth stirring all the time until you get a pile of noodles and sauce with egg curds. Top with sliced scallions and a good grinding of black pepper.