Stuffed grape leaves are the perfect appetizer or addition to a potluck spread. Buy grape leaves in 16-ounce jars that contain about 80 leaves, which will provide plenty of large, well-shaped leaves to work with. Slideshow: More Mediterranean Recipes
Place rice in bowl and rinse under cold running water until water runs clear, about 2 minutes. Add water to cover by 1 inch, and let stand 20 minutes. Rinse and drain rice.
Stir together the parsley, tomatoes, scallions, white onion, and mint in a large bowl. Add rice. Stir together 1 cup oil, lemon juice, tomato paste, and salt in a separate bowl. Add oil mixture to parsley mixture, and stir until well combined.
Separate grape leaves, and gently rinse with water. Working with 1 grape leaf at a time, lay leaf on a work surface with the stem facing toward you and the rough side facing up. Place 1 1/2 to 2 tablespoons of parsley mixture in center of leaf. Firmly fold leaf away from you and over filling, then fold the left and right sides of the leaf over filling. Roll leaf up and away from you while keeping filling pressed in a tight log. Repeat procedure with remaining grape leaves and filling.
Spread remaining 1 tablespoon oil in the bottom of a 12-inch, high-sided skillet with a tight-fitting lid. Line potato slices on bottom of prepared pan. Place stuffed grape leaves, seam side down with sides of leaves just touching, in a circular pattern on potatoes (stuffed grape leaves will be stacked in multiple layers). Place a large, flat ovenproof plate on grape leaves, and press gently. Pour any drippings from bowl into pan, and add just enough water to barely cover grape leaves.
Bring to a boil over high; reduce heat to medium-low, and cover tightly with lid. Cook until grape leaves are tender and rice is cooked through, 30 to 35 minutes. Test doneness by removing one stuffed grape leaf from liquid and cutting it in half to taste. When stuffed grape leaves are done, remove lid and, using tongs, remove plate and stuffed grape leaves. Let stand 5 minutes before serving. Serve potatoes with a slotted spoon.