Preheat oven to 375°F (190°C).
In a pan, sauté shallots and garlic in olive oil until soft.
In a bowl, combine mozzarella and cheddar. Set aside 1 cup for topping.
In a 9x13-inch baking dish, layer ¼ of the zucchini, followed by ¼ of the shallot mixture, ¼ of the cheese mix, and ¼ of the sour cream. Season with salt, pepper, and thyme. Repeat layers three more times.
Mix panko with melted butter, reserved cheese, and Parmesan. Sprinkle over the casserole.
Bake for 40-45 minutes until golden and bubbly.
If desired, broil for 2-3 minutes for a crispier top.
Let rest for 10 minutes before serving hot.
