Place the rice in a large bowl, and cover it with cold water. Massage the rice under the water to release starch, and then drain and rinse the rice under cold running water in a wire mesh strainer for about a minute until the water turns clear. Let the rice drip dry.
Place the rice in a mixing bowl and add the tomato, onion, parsley, mint, tomato paste, olive oil, lemon juice, pomegranate molasses, allspice, cumin, black pepper, cinnamon, Aleppo pepper, and salt. Stir everything together thoroughly.
Carefully separate the grape leaves and rinse them under cool water to remove excess brine. If any leaves have thick stems attached, trim them away with a small knife or sharp kitchen scissors. Arrange the leaves on a work surface with the vein side facing upward and the stem end closest to you.
Place a small portion of filling (about 4 teaspoons or more depending on the size of the grape leaves) near the stem end of each leaf. Fold the bottom of the leaf over the filling, fold in the sides, and roll tightly toward the tip to form a compact cylinder. Continue with the remaining leaves and filling.
Arrange the garlic cloves in the center of a wide heavy pot. Place the rolled grape leaves seam-side down around the garlic, arranging them in a tightly packed layer to prevent unrolling during cooking.
Drizzle the olive oil and lemon juice evenly over the grape leaves, then pour in the water. Set a heatproof plate directly on top of the rolls to keep them submerged during cooking.
Bring the liquid to a gentle simmer over medium heat. Reduce to low heat, cover the pot, and cook for 40-45 minutes until the rice is tender and the grape leaves are fully cooked.
Remove the pot from the heat and leave the grape leaves to rest, covered, for 20 minutes. Transfer them to a serving platter and garnish with parsley and pomegranate seeds. Serve with lemon wedges alongside.