Melt the butter in a large pot over medium heat. Add the onions and garlic and cook, stirring frequently, until soft and translucent, about 8 minutes. Do not brown; reduce the heat if necessary.: The air will fill with a warming, slightly sweet aroma as the onion sweats and loosens its sugars, and the garlic will give off a gentle perfume. You should see the onion turn glossy and pale, not browned, which signals the right stage. Stir frequently so nothing sticks, and keep the heat moderate to avoid browning, which would change the flavor profile. If you notice any browning, lower the heat and add a splash of broth to deglaze the pan. A common mistake here is rushing the step with high heat, which yields bitter, toasted notes instead of the intended soft, sweet base.
In the meantime, cut the tips off of one bunch of the asparagus and set aside (you'll use those for a garnish). Cut the remaining spears and the other bunch of asparagus into 1/2-inch (13-mm) pieces.: Cutting the asparagus releases its fresh, green scent and readies it to cook through evenly. The reserved tips will remain vibrant and tender when blanched later, so set them aside carefully. Uniform pieces ensure consistent texture after simmering. Avoid using woody bottoms in the soup; discard or compost them, as they stay fibrous. If pieces are uneven, you risk some becoming mushy while others remain undercooked.
Add the chopped asparagus to the pot (minus the reserved tips), along with the chicken broth, 1 teaspoon salt and 1/4 teaspoon pepper. Bring to a boil, then cover and turn the heat down to low. Simmer for about 30 minutes, or until the vegetables are very tender.: As the pot comes to a gentle boil, it will steam and the broth will take on a pale green hue. Covering helps coax tenderness while conserving flavor. When you lift the lid, the aroma should be fresh and vegetal, and the spears should yield easily to a fork. This long, slow simmer softens fibers so the final puree is silky. If the soup tastes flat after simmering, it usually means it needs more salt or a squeeze of lemon . A common pitfall is undercooking the vegetables, which produces a gritty texture after pureeing.
Meanwhile, bring a small pot of salted water to a boil. Cook the reserved asparagus tips for a few minutes, or until tender-crisp. Drain the tips and then place them in a bowl of ice water to 'shock' them—this stops the cooking process and preserves their bright green color. Once the tips are cool, drain them and set aside.: The brief blanch and immediate ice bath lock in the vibrant color and snap of the garnish, and the contrast between soft soup and crisp tips is delightful. When you bite one of the blanched tips, it should offer a quick, fresh snap rather than limp mush. Be careful not to overcook here, since the tips will finish warming when added to the bowls. Overblanching leads to dull color and a flabby texture.
Purée the soup with an immersion blender until completely smooth. (Alternatively, use a standard blender to purée the soup in batches, then return the soup to the pot.) Bring the soup back to a simmer and stir in the lemon juice and Parmigiano-Reggiano. Taste and adjust seasoning, if necessary. To thicken the soup, allow it to simmer, uncovered, until the desired consistency is reached.: The moment you puree, the kitchen fills with a concentrated green aroma, and the texture transforms into a velvety, ribbon-like consistency. If using a blender, fill it only halfway and vent the lid slightly to release steam safely. After returning to the pot, the lemon will lift the flavors while the Parmigiano-Reggiano melts into a savory silk. If the soup feels too thin, a gentle simmer will reduce it and intensify flavor, but avoid vigorous boiling which can dull the lemon's brightness. A frequent error is overheating after adding cheese, which can cause the dairy to separate and grain the texture.
Ladle the soup into bowls, then top each bowl with asparagus tips, Parmigiano-Reggiano, herbs (if using), and freshly ground black pepper.: The final assembly is about contrast and finishing touches. Spoon the pale green soup into warm bowls so it stays hot longer, then artfully scatter the blanched tips for color and texture. A final grating of Parmigiano-Reggiano melts slightly and adds shimmering flecks, while a few turns of black pepper give a gentle lift. If you notice the soup separating or looking oily, it likely overheated when the cheese was added; gently whisking off heat usually brings it back together. Presentation matters, and a neat garnish makes the bowl feel restaurant-worthy.