Preheat oven to 400°F (200°C).
In a large bowl, toss shredded potato with beaten egg, salt, pepper, and Parmesan until evenly coated.
Generously grease a 12-cup muffin tin. Press potato mixture firmly into each cup, forming hollow nests.
Bake 20-25 minutes until deeply golden and crisp around edges.
Spoon shredded chicken into each par-baked nest and top with shredded cheese.
Bake 8-10 minutes more until cheese is melted, bubbling, and spotty gold.
Let rest 5 minutes in tin, then loosen edges and serve hot.
