Make gremolata topping: On a cutting board, mince garlic, then add lemon zest on top of garlic, and place parsley leaves on top of lemon zest. Chop everything until the parsley is finely cut, and the mixture almost resembles a paste. Set aside.
Make casserole: Preheat oven to 350°F. In a double boiler with the lid on, steam squash and onions for about 5 minutes, or until centers of squash become transparent and tender.
Remove from heat, drain if necessary, and transfer to a large metal bowl. Mash with a potato masher or fork. Stir in cheese, butter, sugar, milk, 1 cup breadcrumbs, and eggs. Season with salt and pepper.
Assemble casserole: Mix remaining breadcrumbs with gremolata and 1 tablespoon olive oil or melted butter. Place squash mixture in a buttered casserole dish, and evenly sprinkle gremolata breadcrumbs on top.
Bake for 25-30 minutes or until eggs set. Let sit out for 20-30 minutes before slicing and serving.
