Slice the yellow squash into rounds, about 1/4 inch thick. You can also cut the squash into half-moons if preferred.
In a large skillet, melt the butter over medium heat. Add the sliced squash and chopped onion. Sauté for about 5-7 minutes, or until the squash is tender and the onion is softened. Remove from heat and set aside to cool slightly.
Make the Casserole Mixture:
In a medium bowl, combine the sour cream, mayonnaise, garlic powder, Parmesan cheese, and shredded cheddar cheese. Stir until everything is well mixed.
Add the cooked squash and onion mixture to the bowl. Season with salt, pepper, and dried thyme (if using), and stir gently to combine.
Assemble the Casserole:
Transfer the squash mixture into a greased 9×13-inch baking dish and spread it evenly.
In a small bowl, mix the breadcrumbs or crushed crackers with 1/4 cup of grated Parmesan cheese. Sprinkle the mixture evenly over the top of the casserole.
Bake:
Preheat the oven to 350°F (175°C). Bake the casserole for 25-30 minutes, or until the top is golden brown and the casserole is bubbly around the edges.
Serve:
Let the casserole cool for a few minutes before serving. Garnish with fresh parsley for added color and flavor.