Drain the grape leaves, rinse under cool water, and pat dry with paper towels.

In a large bowl, combine uncooked rice, parsley, mint, dill, minced onion, 2 tablespoons olive oil, salt, pepper, cumin, and cayenne; mix until evenly distributed.

Place a grape leaf shiny side down on a board with the stem end toward you. Add 1 tablespoon of filling near the stem, fold sides over, and roll tightly away from you to form a cylinder.

Repeat with remaining leaves and filling, making about 24 rolls.

Coat the bottom of a medium saucepan with the remaining 1 tablespoon olive oil. Arrange rolls seam side down in tight concentric layers.

Pour vegetable broth and lemon juice over the rolls; liquid should nearly cover them.

Cover, bring to a boil over medium-high heat, then reduce to low and simmer gently for 45 minutes until rice is tender.

Remove from heat and let rest, covered, for 10 minutes before serving warm or at room temperature.