Preheat oven to 350 degrees F (175 degrees C). Grease an 8-inch pie pan with cooking spray.
Whisk eggs and milk together in a bowl. Season with black pepper and dill.
Place potato nuggets in a large skillet over medium heat; cook and stir until almost thawed, about 5 minutes. Add corned beef and onion; cook and stir until onions are translucent, about 5 minutes. Remove from heat and cool briefly, about 5 minutes.
Stir potato nugget mixture into egg mixture. Fold in Cheddar cheese and Parmesan cheese. Pour into pie pan.
Bake in the preheated oven until eggs are firm and cheeses are melted, about 30 minutes.