Boil the potatoes, then peel and force through a potato ricer. Spread onto a pastry board and let cool.
Add the sifted flour, eggs, one tablespoon of butter and a pinch of salt. Knead together.
Shape the dough into a roll and divide into pieces about 6 inches long. Press each piece of dough into a large enough square to wrap around an apricot.
With lightly floured hands, wrap the apricot (pitted and pressed closed) with the dough and form a ball. Drop the “dumplings” into a large pot of boiling salted water. Boil until they float to the surface. Remove with a slotted spoon and drain.
In a separate pan, melt the remaining butter. When it begins to brown, stir in the breadcrumbs. After a minute or two, add the dumplings.
Turn with a wooden spoon in the butter to coat evenly. Dust with sugar and cinnamon, and serve hot.