1. Heat 1 tablespoon olive oil in a small skillet over medium-high heat. Add onion and cook, stirring, until translucent. Add garlic and cook, stirring, for 1 minute. Remove from heat and add mixture to a large bowl, along with cooked rice, parsley, mint, lemon zest, currants, and pine nuts; stir to combine. Add 1 tablespoon olive oil, 2 tablespoons lemon juice, 1 teaspoon salt, and 1/2 teaspoon pepper to bowl; stir to combine and set aside.

2. Preheat oven to 325 degrees. Place one grape leaf on work surface, vein-side up. Place 1 heaping tablespoon rice mixture in the center of grape leaf. Roll leaf from bottom up, folding in sides to form a 2-inch log. Place seam side down in a 9-by-13-inch baking dish. Repeat process with remaining grape leaves and rice mixture.

3. In a large bowl, mix together chicken broth, remaining 2 tablespoons lemon juice, and remaining 3 tablespoons olive oil; pour over grape leaves. Top grape leaves with lemon slices. Place a second 9-by-13-inch baking dish on top of grape leaves and lemon slices and fill halfway with water to weight down. Carefully transfer to oven and bake until grape leaves are tender, 40 to 50 minutes. Serve immediately.