Mix the cinnamon, 4 teaspoons salt and 1/2 teaspoon pepper in a bowl; sprinkle all over the hens and inside the cavities. Place the hens on a rack set on a rimmed baking sheet and refrigerate, uncovered, at least 2 hours or overnight. Meanwhile, soak the grape leaves in water 1 hour.
Bring the chicken broth and 2 cups water to a boil in a saucepan; add the rice blend and cook as the label directs. Drain and rinse under cold water.
Preheat the oven to 400 degrees F. Melt 4 tablespoons butter in a large skillet over medium-high heat. Add the shallot, garlic, ginger and cumin and cook, stirring, until soft, about 3 minutes. Remove from the heat; add the cooked rice, pomegranate seeds, and chopped parsley and cilantro; toss to coat. Season with salt and pepper. Add the egg yolks and stir to combine.
Make the glaze: Bring the orange juice and pomegranate molasses to a boil in a small skillet over medium heat. Cook until reduced by half, about 5 minutes. Remove from the heat and swirl in the remaining 2 tablespoons butter.
Fill the cavity of each hen with about 1/2 cup of the rice mixture (reserve the rest); tie the legs together with twine. Roast 20 minutes, then brush with the pomegranate glaze. Continue roasting, glazing every 10 minutes, until a thermometer inserted into the thigh registers 165 degrees F to 170 degrees F, 1 hour to 1 hour, 10 minutes. (Rotate the hens halfway through cooking; if the skin gets too dark, cover loosely with foil.)
Meanwhile, drain the grape leaves and pat dry. Use some of the leaves to line a 9-inch pie dish. Fill with the reserved rice mixture and drizzle with 2 tablespoons water. Cover with the remaining grape leaves, shiny side up, then cover with foil. (If you aren't using grape leaves, spoon the rice into a pie dish, sprinkle with water and cover with foil.) After the hens have roasted about 20 minutes, transfer the rice to the oven and cook until heated through, about 45 minutes.
Transfer the hens to a platter and add some parsley and cilantro sprigs and pomegranate seeds. Peel the grape leaves off the top of the rice and serve alongside the hens.