Trim the woody ends off the asparagus and rinse them well. Slice the tender spears into smaller pieces, saving the tips for garnish.
Peel and dice the potatoes into 1-inch chunks, ensuring they cook evenly and quickly in the simmering broth.
Heat the olive oil in a large heavy-bottomed pot over medium heat until it shimmers and begins to smell fragrant.
Add the minced garlic and sauté for about 30 seconds until it becomes fragrant and just starts to turn golden.
Stir in the diced potatoes and cook for 3-4 minutes, stirring often, until they start to soften and turn translucent at the edges.
Pour in the vegetable stock, bringing the mixture to a gentle boil. Reduce the heat to low, cover, and simmer for 15-20 minutes until the potatoes are very tender.
While the soup simmers, blanch the asparagus tips in boiling water for about 2 minutes until vibrant green and slightly crisp. Drain and set aside.
Once the potatoes are tender, add the asparagus pieces to the pot, then use an immersion blender to blend the soup until completely smooth and velvety. Alternatively, transfer carefully to a blender in batches, then return to the pot.
Stir in the lemon juice and season with salt and pepper to taste. Let the soup simmer uncovered for another 2 minutes to meld the flavors.
Taste the soup and adjust seasoning if needed, adding more salt, pepper, or lemon for brightness.
Ladle the hot soup into bowls, garnish with the reserved asparagus tips, and finish with a drizzle of olive oil or a crack of black pepper for an inviting presentation.
