Preheat the oven to 400°F (200°C) and thoroughly grease a 12-cup standard muffin tin with cooking spray or oil.
Place the grated potatoes in a clean kitchen towel and squeeze firmly to remove as much moisture as possible.
In a large mixing bowl, combine the squeezed potatoes, beaten egg, Parmesan cheese, salt, and pepper.
Divide the potato mixture into the muffin tin cups, pressing the mixture firmly against the bottoms and sides to form a nest shape.
Bake the potato nests for 20 to 25 minutes, or until the edges are golden brown and the structure is set.
While the nests are baking, heat the vegetable oil in a large skillet over medium-high heat.
Add the ground beef to the skillet and cook until browned, breaking it into small crumbles with a spatula.
Add the diced onion, garlic, and bell pepper to the beef and sauté for 5 minutes until the vegetables have softened.
Stir in the tomato sauce and dried oregano, then reduce heat to low and simmer for 5 minutes.
Remove the potato nests from the oven and spoon the beef mixture into each cavity.
Top each nest with shredded cheddar cheese and return to the oven for 5 to 7 minutes until the cheese is melted and bubbling.
Allow the nests to cool in the tin for 5 minutes before carefully lifting them out with a small offset spatula or knife.