Preheat the oven to 350°F/180°C and prepare a large pie plate (10-12") with cooking spray.
Use a vegetable peeler to remove alternating strips of zucchini peel. Cut the squash into 1/4" or thinner pieces. Use a mandoline for best results.
Heat butter in a large skillet or dutch oven and saute the onions until they soften and begin to change color.
Add the zucchini slices, baked ham and fresh thyme. Stir to coat in the butter and distribute the onions. Cook briefly to warm through. Season with salt and pepper.
Transfer the zucchini mixture to the prepared pie plate, avoid transferring any liquid that may have accumulated.
Pour the eggs over the zucchini and use a spoon to open up space in the mix to allow the eggs to spread.
Bake for 30 minutes then top with the shredded cheese. Bake for another 10 - 15 minutes or until the eggs are set and the top is golden brown.
The zucchini will release more liquid as it bakes. Allow the pie to stand for at least 15 minutes before cutting it into 8 pieces.