Preheat your oven to 350°F (175°C).

In a large skillet, heat the olive oil over medium heat. Add the chopped onion and garlic, sautéing until the onion is translucent, about 3-4 minutes.

Add the sliced yellow squash and zucchini to the skillet. Cook for an additional 5-7 minutes, stirring occasionally, until the vegetables are tender.

Stir in the corn, salt, black pepper, and dried thyme. Cook for another 2-3 minutes, then remove from heat.

In a large bowl, combine the sautéed vegetable mixture with the sour cream and half of the cheddar cheese. Mix well.

Transfer the mixture to a greased 9x13 inch baking dish. Spread it evenly.

Top the casserole with the remaining cheddar cheese, crushed crackers, and grated Parmesan cheese.

Bake in the preheated oven for 25-30 minutes, or until the top is golden brown and bubbly.

Remove from the oven and let it cool for 5-10 minutes before serving.