In large skillet over high heat, cover and cook zucchini, spinach, mushrooms, and garlic, until spinach starts to thaw, about 3 or 4 minutes. With fork, break spinach apart. Uncover and cook, stirring occasionally, until zucchini is crisp-tender, about 5 to 6 minutes. Drain well. In large bowl, beat together eggs, cottage cheese, and seasonings until well blended. Stir in ham and cooked vegetables.
Lightly spray 12 x 7 1/2 x 2-inch baking dish. Pour in egg mixture. Sprinkle with shredded cheese. Bake in preheated 350ºF oven until knife inserted near center comes out clean, about 25 to 35 minutes. Let stand 5 minutes before serving.