If using fresh grape leaves, Prepare an ice water bath and set aside. To prepare grape leaves, bring a medium pot of water to a rolling boil over high heat, add grape leaves, and cook for 5 to 10 minutes (depending upon the size of the leaves) or until leaves are tender but still hold their shape.
Remove grape leaves from the water and submerge them in the ice water bath. Drain.
If using jarred grape leaves, place leaves in a strainer and discard the liquid. Carefully separate the leaves, rinse with cold water, and let drain.
Combine all remaining ingredients except 2 tablespoons of the olive oil and the chicken broth in a medium bowl, and mix until thoroughly combined.
Lay out one grape leaf and remove the tough stem. Place 2 to 3 teaspoons (depending upon the size of the leaf) of filling in the center.
Carefully fold the top and sides of the leaf over the filling.
Roll tightly into a cylinder (it should look like a miniature football).
Arrange dolmathes side by side in a medium saucepan until the bottom of the pan is completely covered. Continue layering dolmathes until they are all in the pan. Add chicken broth and remaining 2 tablespoons olive oil.
Cover the pan and cook over medium heat until dolmathes are cooked through, about 35 minutes. Remove dolmathes to a serving platter, and measure remaining cooking liquid, reserving 1 cup to make the avgolemono sauce. Cover dolmathes loosely with foil to keep warm.