Preheat oven to 350F degrees.
Slice the squash about 1/4-inch thick circles. If some of the squash is large, cut those slices in half.
Slice the onion into 1/4-inch circles, then in half crosswise and break them apart. Cut them even a little smaller, if you like.
Place the squash and onion in a medium-size pot and add enough water to almost cover them. (You can also steam them with a steamer basket.) Cover and bring them up to a boil. Cook 5 minutes or just until they have softened slightly. They will continue to soften and cook when baked in the casserole.
Drain well in a colander.
Meanwhile, whisk the eggs in a medium-size bowl with a fork or whisk. Gradually stir in the milk, then cheese and salt.
Stir in 2 tablespoons of the fresh or dry breadcrumbs. (This helps to slightly thicken the creamy "sauce".
When cool enough to touch, pat the squash and onion dry with paper towels to remove the moisture. Then, add them to the egg mixture.
Pour the squash mixture into an 8x8-inch baking dish or 1 1/2-quart casserole dish that has been greased with butter or coated with oil spray.
Add melted butter to the remaining breadcrumbs. I usually use my fingers to gently mix in the butter. Lightly sprinkle the buttered breadcrumbs over the squash mixture.
Bake for 30 to 35 minutes or until bubbly around the edges and the top is crispy and golden.