Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish with cooking spray or a little olive oil.
In a large skillet, heat the olive oil over medium heat. Add the chopped onion and minced garlic, sautéing until the onion is translucent, about 3-4 minutes.
Add the sliced yellow squash and zucchini to the skillet. Cook for another 5-7 minutes until the vegetables are tender but still slightly crisp. Remove from heat and let cool slightly.
In a large mixing bowl, combine the corn, shredded cheddar cheese, milk, eggs, salt, black pepper, and dried thyme. Whisk until well combined.
Stir in the sautéed vegetables into the egg mixture until evenly distributed.
Pour the mixture into the prepared baking dish. Evenly sprinkle the breadcrumbs over the top.
Bake in the preheated oven for 30-35 minutes, or until the casserole is set and the top is golden brown.
Remove from the oven and let it cool for about 10 minutes before serving.