Preheat the 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 diced onion and minced garlic, sautéing until the onion is translucent, about 3-4 minutes.

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

In a large bowl, combine the sautéed vegetables, shredded cheddar cheese, sour cream, salt, black pepper, and dried thyme. Mix well until everything is evenly combined.

Pour the mixture into the prepared baking dish. Evenly spread the crushed crackers on top, then sprinkle the grated Parmesan cheese over the crackers.

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

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