Bring a large pot of salted water to boil. (The water should appear cloudy from the salt.) Add the pasta and cook until al dente, about 8 to 9 minutes. Drain pasta, saving 1/2 cup of the pasta water.
Meanwhile, cook the bacon over medium-high heat in a large sauté pan until crisp,about 5 to 6 minutes. Remove the bacon with a slotted spoon to a paper-towel-lined plate. Pour off all but 1 tablespoon of the bacon grease.
Sauté the garlic and shallot for 1 to 2 minutes, or until fragrant and softened (do not brown). Add the greens and cook, stirring constantly, for 2 to 3 minutes or until softened. Season with salt and pepper to taste.
Whisk the egg and the Parmesan together in a small bowl. Season with pepper.
Add the drained pasta back into the pot along with the egg and Parmesan mixture. Toss quickly with tongs, adding some of the pasta liquid to thin the sauce out a bit (I used about 3 tablespoons), until all the pasta strands are coated evenly. Add the bacon and the greens, tossing well.
Season with additional pepper, if desired, and serve in bowls with freshly grated Parmesan.