Soak noodles: Place noodles in a large bowl and cover with very hot tap water. Let sit until pliable, while you prepare the rest of the ingredients, at least 20 minutes.
Prep tamari sauce: In a small bowl, whisk tamari, Sriracha, 3 tablespoons of the brown sugar (save rest for own use), and juice of half the lime (about 1½ tablespoons). Cut the other lime half into wedges.
Prep ingredients: Grate carrot on the large holes of a box grater (no need to peel). Trim ends from ⅔ of the scallions and thinly slice , keeping dark greens separate. Peel and finely chop 2 teaspoons garlic. Coarsely chop peanuts.
Cook eggs: Beat 2 large eggs with a pinch of salt in a small bowl. Heat 2 teaspoons oil in a large nonstick skillet over medium-high, tilting to coat skillet. Add eggs and cook, stirring gently, until scrambled, about 2 minutes. Remove from skillet and chop into small pieces if needed. Wipe out skillet.
Cook aromatics: Heat 2 tablespoons oil in the same skillet over medium-high. Add carrots, scallion whites, and garlic and cook, stirring constantly, until fragrant, about 1 minute. Season to taste with salt.
Finish & serve: Drain noodles well. Add to skillet with tamari sauce and 1 cup water. Cook over medium-high heat, tossing frequently, until liquid is nearly evaporated, 5–7 minutes. Add eggs, increase heat to high, cook until noodles are slightly browned in spots, 2 minutes. Off heat, fold in spinach to wilt. Serve with lime wedges, scallion greens, and peanuts. Enjoy!