In a large pot or Dutch oven, melt the butter over medium heat. Add the chopped onion and celery and cook until softened, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.

Add the diced potato, asparagus, peas, and vegetable broth to the pot. Bring to a boil, then reduce the heat to a simmer. Cover and cook for 15-20 minutes, or until the potatoes and asparagus are very tender.

Carefully transfer the soup to a high-speed blender in batches. Blend until completely smooth and velvety. Alternatively, use an immersion blender directly in the pot.

Return the blended soup to the pot over low heat. Stir in the heavy cream, fresh dill, salt, and pepper. Heat gently, but do not let it boil.

Stir in the fresh lemon juice just before serving. Taste and adjust seasoning if necessary. Garnish with extra dill, a swirl of cream, or homemade croutons.