Heat the olive oil in a large soup pot over medium heat. Add the chopped white ramp bulbs to the pot. Stir them around and cook them until slightly softened, about 2 minutes.
Add the diced potato, asparagus and cayenne. Sauté the vegetables for a minute or so. Add the white wine, let the alcohol burn off a bit and stir the vegetables some more. Season everything with salt and pepper. Keep cooking the vegetables until the asparagus is bright, bright green, about 4 minutes.
Add the vegetable stock to the pot (enough to cover by an inch or so) and bring the mixture to a boil. Simmer the soup until the potatoes are just tender, about 15 minutes or so. Add the chopped ramp greens and stir. Simmer until the ramp greens are bright and softened, about 2 minutes. Remove the pot from the heat.
Carefully blend the soup in batches in your blender to purée. Add the blended soup back to the pot. Add the lime juice to the puréed soup and stir to combine. Check the soup for seasoning and adjust if necessary (more salt, lime etc). To serve, bring the pureed soup to a boil and serve with any garnishes you like.