Cook the papardelle in salted boiling water until al dente. Strain.
Heat the extra-virgin olive oil in a pan over medium heat. Add the smashed garlic to the pan and saute until golden and fragrant, about 2 minutes. Throw in the baby asparagus, shiitake mushrooms, and Thai chile. Saute for 8 minutes or until the veggies are tender but still crisp. Add the tomatoes to the pan and season generously with sea salt, freshly ground pepper and brown sugar. Give it a good stir and then let the tomatoes sauce up for about 8 to 10 minutes. Add the cooked pasta and prosciutto to the pan, mix it up for a couple of minutes so that the flavors meld together.
Serve the pasta topped with freshly-grated Parmesan cheese.