Preheat your oven to 200°C (390°F). Toss the trimmed asparagus spears with a little olive oil, salt, and pepper, then spread them on a baking sheet. Roast for 12-15 minutes until slightly caramelized and fragrant. This deepens the flavor with a smoky, sweet aroma.
While the asparagus roasts, peel and dice the potatoes into 1-inch cubes for even cooking. Rinse and set aside.
In your large pot, heat the olive oil over medium heat until shimmering. Add the chopped onion and cook, stirring occasionally, until translucent and fragrant, about 5 minutes. The onion should turn a soft, golden color and smell warm and inviting.
Add the minced garlic to the pot and cook for another minute, until fragrant but not browned. It should release a sweet, pungent aroma.
Add the diced potatoes to the pot and pour in the vegetable stock, enough to cover the vegetables. Bring the mixture to a gentle simmer over medium heat, around 85°C (185°F). Cook for 15-20 minutes, until the potatoes are fork-tender and start to break down slightly, filling your kitchen with a warm, earthy smell.
Once the potatoes are tender, add the roasted asparagus to the pot. Use an immersion blender to blend everything until smooth and velvety, or transfer in batches to a blender. Blend until the soup is silky, with no lumps, and has a vibrant green hue. If it seems too thick, stir in a little more hot broth until you reach your desired consistency.
Season the soup with salt and pepper to taste. Stir in a splash of fresh lemon juice to brighten the flavors and add a lively citrus note. If desired, swirl in a spoonful of cream or sour cream for added richness and tang.
Let the soup rest off the heat for 3-5 minutes to allow flavors to meld. Ladle into bowls, garnishing with reserved roasted asparagus tips or a drizzle of olive oil if you like. Serve hot and enjoy the fresh, velvety texture.