Warm the olive oil over medium-low heat in a dutch oven.
Add in the onions, leek, potatoes and carrots; season with salt and pepper and cook, stirring gently, for 5 minutes, or until veggies begin to soften a bit.
Stir in the garlic and cook for 1 minute.
Mix in the broth.
Toss in zest and lemongrass.
Increase heat and bring soup to a boil, then lower heat and simmer gently, uncovered, until the vegetables are just short of tender, about 10 to 12 minutes.
With the soup at a gentle simmer, drop in the asparagus and mushrooms; cook until tender, about 5 minutes.
Add spinach over the vegetables and cook another 2 minutes, just until slightly wilted.
While the vegetables are simmering, slip the eggs into a pot of simmering water and boil to desired doneness.
Taste finished soup for seasonings and adjust accordingly.
Ladle the vegetables and broth into shallow soup plates, scatter with chopped fresh herbs, and finish each with a poached or boiled egg on top; serve immediately.