Cut around core of cabbage with a knife, and remove core. Place cabbage, core side down, in a large, 3-quart pot. Cover cabbage with water, set over high heat, and cook for 30 minutes. Drain cabbage, set aside to cool, and separate leaves. (You need 24 leaves.)
In a large bowl, combine long-grain rice, zucchini, 1 tablespoon garlic, 1 teaspoon salt, and [1/2] teaspoon black pepper.
In a 2-quart pot, combine tomato sauce, water, remaining 3 tablespoons garlic, mint, remaining 1 teaspoon salt, and remaining [1/2] teaspoon black pepper.
Lay each cabbage leaf flat on your work surface, spoon 2 tablespoons filling on each leaf, and roll leaf. Layer rolls in a large pot, pour sauce into the pot, cover, and cook over medium-low heat for 1 hour.
Let rolls rest for 20 minutes before serving warm with Greek yogurt.
Notes
Tasty Tip If the cabbage leaves are too big, you can cut them in half and make 2 rolls from 1 leaf.