Preheat the oven to 400°F. Prick the sweet potatoes all over with a fork and put them on a baking sheet. Roast until completely soft, 1 to 1-1/4 hours. Let stand until cool enough to handle.
Halve the sweet potatoes and scrape the flesh into a large bowl. Refrigerate until cool.
Add 1 cup of the flour, the egg, salt, and pepper to taste to the sweet potatoes and mix until a soft dough forms. Turn out onto a well-floured work surface and knead gently until the dough is smooth and no longer sticky. (If it is still sticky, add a bit more flour and continue kneading.) Use a bench scraper to keep the dough from sticking and to release it from the work surface. Cut the dough into 6 portions and roll each portion into a long cylinder about 1/2 inch thick. Cut each one into 1/2-inch pieces and transfer to a baking sheet lined with a floured towel.
Bring a large pot of water to a boil and salt it generously.
Meanwhile, heat the oil in a large skillet over medium heat. Add the pancetta and cook until beginning to brown, about 5 minutes. Stir in the onions and cook until softened, 6 to 8 minutes. Transfer the mixture to a small bowl and set aside.
Melt the butter in the same skillet over medium-low heat and cook until the milk solids begin to turn brown and the butter gives off a nutty aroma. Immediately add the vinegar and swirl the pan to combine. Add the kale, stir, and add 1 to 2 Tbs. water to help the leaves wilt. Reduce the heat to low and keep warm.
Reduce the heat under the boiling water to maintain a simmer. Drop the gnocchi into the water and cook until they all float, 8 to 10 minutes. Drain the gnocchi and add to the balsamic brown butter, along with the reserved pancetta and onions. Sprinkle in the chopped sage, season with salt and pepper, and toss well to coat.
Divide the gnocchi among warm shallow bowls and, using a vegetable peeler, shave Parmesan strips over the top. Garnish with sage leaves and serve immediately.