Melt the vegan butter in a large pot or Dutch oven over medium heat. Add the chopped leeks and onions, sautéing until soft and translucent, about 5 to 7 minutes.
Add the diced potato, chopped asparagus stalks (reserve the tips for later), vegetable broth, salt, and black pepper. Bring the mixture to a boil.
Reduce the heat to low, cover the pot, and simmer for 15 to 20 minutes, or until the potatoes and asparagus stalks are very tender.
While the soup simmers, steam or blanch the reserved asparagus tips in a small pan of boiling water for 2 to 3 minutes until tender-crisp. Drain and set aside for garnish.
Remove the soup from the heat. Use an immersion blender to carefully puree the soup directly in the pot until it is completely smooth and creamy.
Stir in the fresh lemon juice, nutritional yeast, and chopped parsley. Taste and adjust the seasoning if necessary.
Ladle the hot soup into bowls and garnish with the reserved steamed asparagus tips and additional fresh herbs before serving.