Pour the broth into a small saucepan and bring to a gentle simmer on the stovetop.
On another burner, heat the olive oil in a large, wide skillet. Add the shallots and a pinch of salt and sauté, stirring occasionally, until softened, 1 to 2 minutes.
Add the dried pasta and stir it around to coat it in the oil and the shallots.
Use a ladle to transfer about 1 1/2 cups of stock from the saucepan to the pasta skillet.
Cook, stirring gently, until nearly all stock has evaporated. Add another cup of stock, and cook, stirring, until nearly all the liquid has been absorbed, but not all—like you're making risotto. Add more stock from time to time until the pasta is al dente (taste frequently!), about 18 minutes. When your pasta is about 5 minutes from being done, add the asparagus pieces—you want to make sure they're cooked through by the time the pasta is ready.
When the pasta is at the desired firmness, take it off the heat, shower with Parmesan and lemon zest and fold to incorporate. Serve immediately.