If using the baking potato, peel and cut it into 1 inch dice. Cover with water, bring to a boil and reduce heat to a simmer. Cook until soft but not mushy.
Fit a mixer with the whisk attachment and mash the potato. Measure 1 ¼ cups and cool completely.
Alternatively, reconstitute the instant mashed potatoes according to the directions on the box to make 1 ¼ cups. Cool completely.
In the meantime, pit the plums and place a cube of sugar in each void. Set aside.
Add the flour and salt to the mixer bowl. Cut the cold butter into pieces and add to the bowl. Mix at medium until the butter is cut in so it is indistinguishable.
Add the mashed potatoes and mix in completely.
Add the eggs and mix until a soft , slightly sticky dough forms.
Remove it from the bowl and knead it several times to smooth it out.
Lightly flour the work surface and the top of the dough. Roll the dough into a 16”x16” rectangle. It doesn’t have to be perfect. Cut into 4” squares.
Put a plum in the center of the square. Bring each corner up and over the top of the plum. Pinch very well to seal all edges.
Roll between the palms of your hands to make a round dumpling. Cover with a towel if cooking immediately or freeze.
Bring 6 to 8 quarts of water to a boil. Add 1 tablespoons of salt.
While the water is coming to a boil, melt the butter over low heat in a large skillet or sauté pan. Add the breadcrumbs and toast to a medium brown. Stir frequently to prevent over-browning or burning.
Remove from the heat and add the brown sugar. Set aside.
Add about 6 to 8 dumplings to the boiling water. They will sink to the bottom of the pot. Cook 7 to 9 minutes, stirring once or twice to make sure they are not sticking to the bottom of the pot.
Cook for about 7 to 9 minutes if cooking immediately. Add a few minutes if they are frozen. When they rise to the top of the pot, they are done. Immediately remove one at a time from the water with a slotted spoon and transfer to the crumb mixture. Roll gently to coat completely. Repeat with remaining dumplings. Sprinkle the additional crumbs over the dumplings.