Start by trimming the ends of the summer squash, then slice it thinly to ensure even cooking and to avoid excess watery texture.
Place the sliced squash in a mixing bowl, sprinkle with a pinch of salt, and let it sit for 10 minutes to draw out excess moisture. Then, gently squeeze out the water and pat dry with a paper towel.
In a skillet, heat 1 tablespoon of olive oil over medium heat, then add the diced onion. Sauté until translucent and fragrant, about 5 minutes, stirring occasionally.
Preheat your oven to 375°F (190°C). Lightly toast the panko breadcrumbs in a small skillet with a teaspoon of butter until golden brown and crispy, then set aside.
In a large mixing bowl, whisk the eggs until smooth. Add the chopped thyme, salt, pepper, and grated cheese, mixing well to combine.
Add the sautéed onion and the sliced squash to the egg mixture, gently folding to coat everything evenly.
Pour the mixture into a greased baking dish, spreading it out evenly with a spatula. Drizzle a little olive oil over the top for extra crispness.
Sprinkle the toasted panko breadcrumbs evenly over the top of the casserole, pressing lightly to adhere.
Bake in the preheated oven for about 30 minutes, until the top is golden-brown and bubbling around the edges.
Remove from the oven and let it rest for a few minutes. The casserole should be tender with a crispy, toasted topping, ready to serve hot.