How to Make It
In a medium saucepan, cover the potatoes with cold water and bring to a boil. Reduce the heat to moderate and cook until tender, 45 minutes. Drain, let cool slightly and peel, then pass through a ricer. Transfer to a plate and let cool.
Transfer the potatoes to a large bowl and make a well in the center. Add the egg and salt to the well; stir in the potatoes. Add 1 cup of the flour; stir until a stiff dough forms. Transfer the dough to a work surface and quickly knead in the remaining 2 tablespoons of flour until a smooth, firm dough forms. Add more flour if the dough is not firm or smooth; the less flour you use, the softer the dough will be.
Roll the gnocchi dough into a log and cut it into 16 pieces. Flatten 1 piece of the dough into a 3-inch round in your palm. Spoon a scant tablespoon of the preserves into the center of the dough and carefully pinch the seams together, rolling and patting the dough into a ball. Pinch together any tears and transfer the ball to a large plate dusted with flour. Repeat with the remaining dough and preserves.
In a large nonstick skillet, melt 4 tablespoons of the butter. Add the bread crumbs and cook over moderate heat, stirring, until golden and very crisp, about 7 minutes. Remove from the heat and stir in the sugar and cinnamon. Transfer the crumbs to a pie plate. Wipe out the skillet.
In a large pot of boiling water, cook half of the gnocchi just until they rise to the surface, stirring once, 5 minutes. Using a slotted spoon, transfer them to a large plate and gently pat dry with paper towels. Repeat with the remaining gnocchi.
Melt the remaining 2 tablespoons of butter in the skillet. Add the gnocchi and cook over moderately high heat, turning once, until lightly browned, about 4 minutes. Add the gnocchi to the pie plate and roll to coat them with crumbs. Transfer to plates and serve at once.