Preheat the oven to 350 degrees F. Grease a 9 by 13-inch baking dish with 1/2 tablespoon butter.

Heat the olive oil and the remaining 1 tablespoon butter in a medium pot over medium-high heat. Add the onions, salt, and black pepper and cook until the onions are soft, about 5 minutes. Add the garlic and cook until fragrant, about 30 seconds. Add the squash and zucchini and cook until tender, stirring occasionally, about 20 minutes. Stir in the thyme and remove from the heat. Using a slotted spoon, transfer the vegetables to the prepared baking dish, reserving the cooking liquid.

Combine the eggs and cream in a medium bowl and whisk to blend. Gradually whisk the reserved cooking liquid into the egg mixture. When all the cooking liquid is incorporated, pour the mixture over the vegetables in the baking dish. Using a spoon, gently shift the vegetables around so the egg mixture is evenly distributed. Bake until the mixture sets, about 30 minutes. Remove from oven and sprinkle first with the crackers and then with the Parmesan, if using, and return to the oven. Bake until golden brown, 10 to 15 minutes.