The best thing I've made with Parmesan broth recently was a kind of cross between a stew and a pasta that paired goat cheese ravioli and spring vegetables. I used asparagus tips and sugar snap peas for this recipe, but I've also made similar dishes with English peas, fava beans, shaved radishes and even bolted lettuce from the garden.
The only part that's even a little tricky is making the ravioli. If that intimidates you (and it shouldn't … it takes less than an hour of work and it's actually really fun), you could substitute quadrati — little fresh pasta squares; make them beautiful by including leaves of fresh herbs on the last turn of the dough.
Gnocchi would work too, but if you insist on dried pasta, use tiny orzo or stelline. This dish emphasizes delicacy; any of the chewier shapes would be out of sync. Cook them separately so they don't cloud the broth.
Most everything can be prepared in advance, so only a few minutes of cooking are needed just before serving. Make the Parmesan broth and the goat cheese ravioli. Prepare and blanch the vegetables.
Then at the last minute reheat the broth and bring a wide pot of water to a boil. Cook the ravioli and divide it among warm pasta bowls. Reheat the blanched vegetables in the same water and arrange them over the ravioli. Ladle over some broth and sprinkle with chopped chives and a little grated Parmesan to finish.