Begin by grating the summer squash using a box grater, then transfer it to a clean kitchen towel or paper towels and squeeze out as much excess moisture as possible. This step prevents a soggy casserole.
Meanwhile, dice the onion and sauté it in a skillet over medium heat with a little oil until translucent and fragrant, about 5 minutes. This softens the onion and brings out its sweetness.
In a large mixing bowl, combine the drained shredded squash, sautéed onions, beaten eggs, chopped herbs, and cream or milk. Stir until well blended; the mixture should be moist but not watery.
Fold in the shredded cheese, distributing it evenly throughout the mixture. The cheese will melt during baking, creating a gooey texture.
Pour the mixture into a greased baking dish, smoothing the top with a spatula for even baking.
Sprinkle the Panko breadcrumbs evenly over the top for a crispy, golden crust.
Bake in a preheated oven at 375°F (190°C) until the casserole is bubbling around the edges and the top is golden brown, about 30 minutes. Keep an eye on it to prevent over-browning.
Once baked, let the casserole rest for 5 minutes, then serve hot, enjoying the tender squash contrasted with crispy topping and melted cheese.