Lay out one grape leaf on a tray with the vein side up. Lay out 1 tablespoon of the rice mixture onto the bottom third of the grape leaf, spreading it into a log shape about 3½-inch wide. Fold the right and left sides of the grape leaf over the rice, then tightly roll up the leaf from the bottom up, making a tight package to create a log shaped stuffed grape leaf. Gently transfer the stuffed grape leaf into the pot with the seam side down. Arrange the stuffed grape leaves tightly in a concentric circle in the bottom of the pot. Repeat the stuffing and shaping process with the remaining grape leaves and rice mixture. Once one layer is filled, place another layer of grape leaves on top.