Preheat the oven to 350ºF and spray a 2-quart casserole dish with nonstick cooking spray.
Add the olive oil to a large skillet over medium heat.
Add the sliced squash, onion and 1 teaspoon salt to the oil and cook, stirring frequently, until the squash is barely softened. Add the garlic and thyme and cook 1-2 minutes more.
Remove the squash from heat and place it in a colander to drain any excess moisture. Let it sit for 5-10 minutes.
Add the non-dairy milk and cornstarch to a large bowl. Whisk together until the cornstarch has dissolved.
Add the remaining 1⁄2 teaspoon salt, sour cream, mayonnaise, black pepper and paprika to the milk. Whisk together until it’s a smooth sauce.
Transfer the drained squash to the bowl with the sauce. Add 1⁄2 cup of shredded cheese. Stir everything together.
Spread the vegetables into the prepared baking dish. Cover with remaining shredded cheese.
Combine the breadcrumbs and melted butter and sprinkle them over the top of the casserole.
Bake in the preheated oven for 30 minutes or until the topping is golden brown and the casserole is bubbly.