Preheat oven to 375 degrees. Spray a 10" spring form pan with cooking spray and cover the bottom with parchment paper.
Set aside 1/4 cup of the green onion and reserve for garnish.
Combine green onions, cheese, flour, thyme, salt and pepper in a medium bowl and toss to blend.
Slice squash about 1/8th inch thick. Peel potatoes and keep them covered in water. Slice them 1/8 " thick just as you are ready to make that layer.
Start with one quarter of potatoes and lay the slices in concentric circles on bottom of the spring form pan. Then layer 1/3 of squash slices in concentric circles on top of potato layer. Sprinkle 2 tsps oil over the squash layer. Layer 1/4 cheese as the next layer. Repeat 2 more times with 1/4 potato, 1/3 squash, 2 tsp oil, 1/4 cheese. Finish with the last quart of potato slices and the last 1/4 cheese.
Cover with foil and bake 40 minutes. Remove foil and bake another 25 minutes until potatoes are tender and cheese is browned.
To serve, garnish with reserved green onion and cut into pie shaped wedges.
Can be made ahead of time and rewarmed at 350 degrees for about 30 minutes.