Preheat oven to 350. On the bottom of the pie plate, sprinkle a light layer of cheddar cheese and put it in the oven just long enough to fully melt. Remove and set aside to cool.
Taking the cheese grater, grate zucchini and use a paper towel to squeeze until most of the moisture is removed. Add to the pie tin, spread evenly across. Sprinkle with about half of the remining cheese.
In skillet, warm olive oil and add chopped shallots, thyme and minced garlic.
When fragrant, add broccoli florets (cut into bite size pieces) and cubed ham. Toss well and let cook until broccoli is tender but not soft.
In mixing bowl, crack eggs and add cream, salt and pepper. Whisk until there are bubbles forming.
Transfer the contents of the skillet into the egg mixture and stir well. Pour over the pie plate and cover with remaining cheese. Be sure that the ham and broccoli are covered. If needed, mix an additional egg and splash of cream to fill the pie plate, but still leaving a bit of room for this to expand-don't fill to the brim!
Place in oven and bake for about 20 minutes, or until the top starts to brown and toothpick comes out clean. Remove and serve immediately, or can be great served cold! Enjoy!