Set a large pot of salted water to boil. In a large skillet, heat the Olive Oil (2 tablespoon) over medium-high heat. When it shimmers, add the Onion (1), immediately turn the heat down to medium, season with Kosher Salt (to taste), and sauté stirring occasionally, until soft and just turning to color, 7 to 10 minutes.
Meanwhile, transfer Fresh Spinach (1 pound) to a colander to drain—it's OK if some of the water clings to the greens.
Add a pinch of Crushed Red Pepper Flakes (1 pinch) to the onions and stir for 30 seconds. Add all of the greens.
Cook over medium to medium-high heat until greens shrink way down—use tongs to flip the greens around and help them wilt. Season with a pinch of Kosher Salt (to taste). Turn off the heat.
Add the Pappardelle Pasta (0.5 pound) to boiling water and cook according to package instructions. Reserve ½ cup (or more) of the pasta cooking liquid.
In a medium bowl or liquid measure, whisk together Large Egg (2), Parmigiano-Reggiano (1/4 cup), and Lemon Juice (1 tablespoon). Whisk ¼ cup pasta water into egg mixture.
Drain pasta and immediately add to the pan with the onions and greens.
Pour egg mixture into pan and toss with tongs to combine, turning heat to low or medium if greens have cooled way down.
Season with Coarse Ground Salt and Pepper (to taste). Taste. Add more lemon or more of the reserved pasta cooking liquid to taste. Sprinkle pasta with more cheese if desired and serve immediately.