Melt the sugar in a saucepan over low heat until it caramelizes. Once the sugar is completely melted, add the butter and stir until smooth.
Add the heavy cream and salt to the caramel, then stir until the mixture is smooth and homogeneous.
In a skillet, toast the breadcrumbs with half of the butter until lightly golden brown.
Lay out the strudel dough sheets individually on a clean kitchen towel. Brush each sheet with a little melted butter, then sprinkle with the toasted breadcrumbs.
Place the salted caramel filling on the strudel sheets, then carefully roll them up. Place the strudels in a lightly buttered baking dish.
Whisk the egg and brush it over the tops 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, until nicely browned and crispy.
Let cool slightly before serving, then slice and serve warm.
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