Preheat oven to 350-f degrees. Prepare an 8x8-inch baking dish, or a deep dish pie plate, with cooking spray.
Over medium high heat, sauté the squash, onion and vegetable oil for about 3-4 minutes, until browned a bit. Flip the squash over to cook the other side and lower the heat to medium. Cook for another 4 minutes. Remove from heat.
In a large mixing bowl, combine the egg and sour cream, mixing well. Add the cooked squash and onions, stirring gently to coat. Add 2/3 of the crushed crackers and 2/3 of the shredded cheese; mix gently.
Scoop the squash mixture into the prepared baking dish. Top with remaining cheese and bread crumbs.
Bake until warmed through completely, about 25 minutes. If you want to get a little color on the bread crumbs, you can turn on the broiler for a minute, being sure to watch closely so it doesn't burn.