Preheat your oven to 350°F (175°C).
In a skillet over medium heat, add olive oil and sauté the onions until they become translucent, about 5 minutes. Add the minced garlic and sauté for another minute until fragrant.
Prepare the squash by slicing it into thin rounds. Add the squash to the skillet and cook for about 5-7 minutes, stirring occasionally, until slightly tender. Remove from heat and let it cool slightly.
In a large mixing bowl, combine the cheddar cheese, mozzarella cheese, sour cream, mayonnaise, salt, black pepper, and thyme. Mix well until combined.
Gently fold the cooked squash and onion mixture into the cheese mixture until everything is evenly coated.
Pour the mixture into a greased 9x13 inch baking dish.
Sprinkle breadcrumbs evenly over the top of the casserole. If desired, sprinkle paprika for added color and flavor.
Cover the baking dish with aluminum foil and bake in the preheated oven for 20 minutes. Remove the foil and bake for an additional 10 minutes, or until the top is golden brown and bubbly.
Once done, allow the casserole to cool for a few minutes before serving.