Boil 8L of water.
Peel potatoes and squash and chop into cubes. Keep squash separate from potatoes.
Add cubed potatoes to boiling water with a pinch of salt and cook for 10 minutes.
Add cubed squash to the pot and cook together with potatoes for another 5 minutes.
Drain.
Add butter and oil into a frying pan with cubed chicken breast. Add 2 tsp salt, 1 tsp pepper and ½ tsp paprika.
Saute for 7 to 10 minutes on medium heat.
Add onions, broccoli and mushrooms.
Continue to saute to release flavors from onions for about 2-3 minutes.
Transfer to a glass casserole dish. Add potatoes.
Beat 3 eggs by hand. Add milk and half and half cream with a pinch of salt.
Pour over meat and potato mixture in a casserole dish.
Shred cheeses and cover the mixture.
Cover with lid and bake for 30 minutes at 370F.
Uncover and continue baking for another 15 minutes.
Remove and serve.