Pit the cherries and set aside.
Combine the rum and sugar, then add them to the cherries, ensuring the fruit absorbs the flavors.
In a skillet, toast the breadcrumbs with half of the butter until lightly golden brown.
Lay out the strudel dough sheets one by one on a clean kitchen towel. Brush each sheet with a little melted butter, then sprinkle with the toasted breadcrumbs.
Distribute the rum cherries evenly over the strudel dough sheets.
Carefully roll up the strudels and place them in a greased baking pan.
Whisk the egg and brush it over the top of the strudels to give them a beautiful golden-brown color during baking.
Bake the strudels in a preheated oven at 350°F (180°C) for 30-40 minutes, or until they are nicely browned and crispy.
Before serving, let them cool slightly, then slice and serve warm.
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