Prepare the Filling: In a saucepan, heat the olive oil over medium heat. Add the chopped onions and cook until translucent, about 3-4 minutes. Stir in the rice and cook for another 2 minutes, ensuring the rice is well-coated in oil.
Add Herbs and Season: To the saucepan, add the dill, mint, lemon zest, salt, and pepper. Pour in 1/2 cup of water and bring to a simmer. Cover and cook until the water is absorbed and the rice is partially cooked, about 10 minutes.
Prepare the Grape Leaves: While the rice is cooking, gently rinse the grape leaves in warm water and pat dry. Trim any thick stems and set aside.
Assemble the Dolmades: Lay a grape leaf flat on a work surface, shiny side down. Place about a teaspoon of the rice mixture near the stem end. Fold the stem end over the filling, then fold in the sides and roll up tightly into a cigar shape. Repeat with the remaining leaves and filling.
Cook the Dolmades: Place the dolmades seam side down in a large skillet. Add the remaining 1/2 cup of water and the juice of half a lemon. Cover and simmer for about 30-40 minutes, until the rice is fully cooked.
Make the Yogurt Sauce: While the dolmades are cooking, combine the Greek yogurt, chopped dill, lemon juice, and minced garlic in a bowl. Season with salt and pepper to taste. Refrigerate until ready to serve.
Serve: Once the dolmades are cooked, remove from heat and let them cool slightly. Serve warm or at room temperature with the lemon and dill yogurt sauce drizzled over or on the side for dipping.