Bring a large pot of salted water to a boil.
Melt butter in a large skillet or shallow saucepan over medium heat. Cook until the butter turns a light brown color and smells nutty. Add rosemary and a pinch of salt, and let sizzle for 30 seconds. Take the sauce off the heat. Drop the gnocchi in the boiling water, and stir. As soon as the gnocchi float to the surface, they are done (30 seconds to 1 minute). Return the brown butter sauce to medium-low heat. Using a slotted spoon, scoop the cooked gnocchi into the brown butter sauce, tossing to coat. Add a pinch of red pepper flakes (to taste) and a splash of the gnocchi cooking water, tossing to combine. Remove from the heat and season to taste with salt.
To finish, top gnocchi with a scattering of chopped hazelnuts and a dusting of fresh Parmesan cheese.