For the gnocchi: Preheat the oven to 400 degrees F.
Bake the potatoes for 1 1/2 hours on a baking sheet; this removes water from the potatoes in order to have lighter, less dense gnocchi. Let cool.
Bring a large pot of salted water to a boil. Cut the potatoes in half and scrape the insides into a mixing bowl. Using a ricer or potato masher, mash the potatoes. Add the flour, Parmesan, egg and some salt and pepper and mix until smooth. Flour a clean surface and roll the dough into long strips. Cut 1-inch pieces and boil for about 1 minute, until the gnocchi start to float. Remove with a slotted spoon.
For the brown butter: In a saute pan, melt the butter over medium-high heat until foamy, 1 to 2 minutes. Add the apricots and sage. Cook until the butter starts to brown, 8 to 10 minutes. Remove from the heat, add the gnocchi and mix.
Transfer to a bowl, top with grated Parmesan and enjoy.