If using Italian prune plums, halve them lengthwise and remove the pits. Fill each cavity with 1/2 teaspoon of the sugar and re-form the plums by pressing the halves together. If using larger plums, halve them crosswise, remove the pits and cut into 1/2-inch dice. Toss the diced plums with 1/4 cup of the sugar.
Prepare gnocchi dough according to the recipe without the pepper or cheese. Bring the water to a boil in a large pot. Meanwhile, on a flour-dusted surface roll the dough under your palms to form a cylinder 2 inches in diameter and slice into 24 rounds. Flatten each into a circle 5 inches in diameter. Place a plum or about 3 tablespoons of the diced plums or 2 tablespoons jam in the center of each dough circle. Gather the dough up around the filling, enclosing it completely without tearing the dough. Pat the dough between your hands to seal and even the gnocchi.
Drop gnocchi in the boiling water. Cook until the dough is tender, stirring gently to prevent sticking, about 8 minutes after they rise to the surface. Meanwhile, in a medium-size skillet, melt the butter and the bread crumbs and toast until golden brown. Remove from heat and stir in remaining 1/2 cup sugar and cinnamon. Transfer to a baking dish.
Remove gnocchi from the water and roll in the bread crumb mixture until all are well coated. Arrange on a serving plate and sprinkle with remaining crumbs.
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