Step 1In a soup pot, simmer the chicken broth, water, garlic, Parmesan rinds and herb trimmings until aromatic and flavorful, about 90 minutes. Strain and return to the soup pot.
Step 2In a wide pot, blanch the asparagus tips in plenty of rapidly boiling, generously salted water until just tender, about 3 minutes. Use a wire skimmer or slotted spoon to transfer them to an ice water bath to stop the cooking, then transfer to a bowl and set aside.
Step 3Cut the sugar snaps in half on a bias, then blanch them in the same way, stopping the cooking with the ice water bath and holding in a separate bowl. (The recipe can be prepared to this point up to 24 hours in advance and refrigerated until ready to use.)
Step 4When ready to serve, warm 6 shallow pasta bowls. Bring the Parmesan broth to a simmer, taste and correct seasoning with salt to taste.
Step 5Bring a large, wide pot of water to a boil. Cook the goat cheese ravioli or fresh pasta squares until the pasta is tender, 3 or 4 minutes. Divide the ravioli among the serving bowls. Warm the asparagus tips in the same pot of water and divide them among the pasta bowls. Warm the sugar snaps in the same pot of water and divide them among the pasta bowls. Sprinkle each bowl with chives and then ladle over roughly one-third cup of hot Parmesan broth. Sprinkle with a little grated Parmigiano-Reggiano and pass the remainder at the table.