Heat the oven to 350 degrees F and lightly grease a 2-quart casserole dish. The dish should be ready before the filling is mixed so the warm squash goes straight from bowl to oven dish.

Warm the vegetable oil in a large skillet over medium heat, then add the yellow squash, vidalia onion, and butter. Cook until the onions look translucent and the squash turns tender but still holds its shape instead of falling apart.

Move the cooked squash mixture to a bowl and stir in the Parmesan cheese, sharp cheddar cheese, and Sour cream, then season with salt and pepper to taste. The residual heat should start melting the cheese, and the mixture will smell buttery and savory.

Spoon the mixture into the prepared casserole dish and scatter the crushed buttery crackers evenly over the top. A level topping helps the casserole brown evenly instead of leaving pale patches and dark corners.

Bake for 20 minutes. The casserole is ready when the cheese is bubbling around the edges and the cracker topping is golden brown.