In an 11- to 12-inch straight-sided skillet, bring 3/4 inch water to a gentle simmer over medium heat.
Crack the eggs into the simmering water (the yolks will just break the surface, so they will stay yellow) and poach until the whites are set but the yolks are still runny, about 3 minutes. Using a slotted spoon, gently transfer the eggs to a plate (if they stick to the pan, gently loosen them with a spatula). Discard the water and clean and dry the pan.
Cook the bacon in the skillet over medium heat, stirring occasionally with a wooden spoon, until just browned and crisp, about 5 minutes. Carefully pour off all but about 2 tsp. of the bacon fat, leaving the bacon in the pan. Add the white and light-green parts of the scallions, the garlic, and ginger and cook, stirring, until just beginning to brown, 1 to 2 minutes. Add the chicken broth, soy sauce, and 1 cup water and bring to a boil, scraping up any brown bits on the bottom of the pan. Add the noodles, separating them with tongs as they soften so they are submerged in the broth, and cook until tender, about 3 minutes.
Divide the spinach among deep soup bowls. Divide the ramen and broth among the bowls. With a spatula, carefully slide the eggs into the bowls, sprinkle with the scallion greens, and serve.