Combine pumpkin puree, flour, Parmesan, egg, salt, pepper, and nutmeg in a large bowl. Mix until the dough just comes together—don't overmix, which toughens the gnocchi terribly.
Dust your work surface generously with flour and divide the dough into four portions. Roll each into a 1/2-inch-thick rope, working gently to keep the texture light throughout.
Cut each rope into 1-inch pieces using a lightly floured knife, creating classic gnocchi shape. Work quickly so the dough doesn't dry out while you're handling it.
Bring a large pot of salted water to a rolling boil, then carefully drop in the gnocchi pieces. Cook for 3-4 minutes after they float to the surface—this savory pumpkin gnocchi reaches perfect tenderness at exactly this timing.
While gnocchi cooks, melt butter in a large skillet over medium heat until it foams slightly. Add minced garlic and cook for 45 seconds until fragrant, then stir in fresh sage and toast for another 30 seconds.
Pour in vegetable broth and heavy cream, bringing the sauce to a gentle simmer. Season with salt and pepper to taste, letting it reduce slightly for 2 minutes while maintaining heat consistency.
Using a slotted spoon, transfer cooked gnocchi directly into the sauce, reserving 1/4 cup pasta water. Gently toss the gnocchi with sauce, adding pasta water as needed to reach silky consistency.
Plate immediately and top with toasted pine nuts, crispy prosciutto, fresh sage leaves, and additional Parmesan. The residual heat keeps everything piping hot while flavors meld together beautifully.