Bring a large pot of lightly salted water to a boil.
Add asparagus and cook until almost tender, 2–3 minutes.
Transfer to a bowl of ice water the pour into a colander to drain. Reserve pot.
Bring chicken stock to a simmer in a large skillet over medium heat; add (green) garlic
Cook, stirring often until the sauce has thickened and garlic has slightly softened, about 3 minutes.
Meanwhile, return pot of water to a gentle simmer and add dumplings (one by one so they don’t crush each other), stirring occasionally, until they’re almost double in size and cooked through and tender, about 4 minutes (dumplings will quickly float to the surface).
Transfer dumplings to skillet; add butter
Add chives and lemon juice.
Season with salt and pepper.
Divide asparagus and dumplings into bowls.
Divide the sauce amongst the bowls, ladling over the dumplings and asparagus
Sprinkle with chives and grana padano and drizzle with olive oil.