Start a pot of salted water for the pasta.
Sauté the sausage in a large heavy nonstick pan, breaking it into small chunks with the spatula. When the sausage is cooked and beginning to brown, remove it from the pan and reserve in a little bowl. Wipe out the pan, then add the olive oil.
Add the minced shallots and garlic and sauté for a minute or so. Then add in the dandelion greens and cook, stirring, over low heat, until they are soft and wilted—3 or 4 minutes.
Meanwhile, cook the pasta to al dente according to the package directions. Before you drain the pasta, ladle out a half cup of the cooking water and reserve it. Drain the cooked pasta and rinse it with hot water.
Return the sausage to the pan with the greens and stir together. Turn off the heat.
Ladle the half cup of the cooking water into the beaten egg and whisk it all together. Whisk in the half and half. Add the pasta to the cooking pan, stir everything, and then add in the egg-water-cream mixture. Toss everything together. Scatter on the grated Parmesan, give everything a final stir. Taste and season with salt, if needed. And that’s it. You’re done. Serve in soup plates, offering extra Parmesan for those, like me, who love cheese.