Peel and dice the pumpkin, then roast in a skillet or oven until completely tender.
Mash the cooked pumpkin with a fork or blend in a food processor. If it's too watery, let it drain slightly.
Melt the butter in a skillet, then lightly toast the breadcrumbs in it until golden brown.
Combine the pumpkin with the sugar and cinnamon, then add the toasted breadcrumbs and mix well.
Lay the strudel dough sheets out individually on a clean kitchen towel. Brush each sheet with a little melted butter, then sprinkle with the toasted breadcrumbs.
Place the pumpkin filling on the strudel sheets, then carefully roll them up. Place each strudel in a lightly buttered 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 nicely browned and crispy.
Let it cool slightly before serving, then slice and serve warm.
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