Carefully remove the grape leaves from the jar, rinse them thoroughly under cold running water to remove excess brine, and snip off any remaining tough stems. Set aside a few torn or imperfect leaves.
In a large mixing bowl, gently combine the ground beef, rinsed rice, diced onion, parsley, dill, mint, half of the olive oil, kosher salt, and black pepper. Do not overmix.
Line the bottom of a large heavy-bottomed pot or Dutch oven with the reserved torn grape leaves. This prevents the dolmades from sticking to the bottom and burning.
Place one grape leaf shiny-side down on a flat work surface with the vein side facing up and the stem end closest to you. Place exactly one tablespoon of the meat and rice filling near the stem end.
Fold the bottom lobes of the leaf up over the filling. Fold in the left and right sides, then roll tightly toward the top tip of the leaf, creating a neat cylinder. Repeat until all filling is used.
Arrange the stuffed grape leaves tightly together in the prepared pot, seam-side down, in a single layer. Pack them snugly so they don't unravel. Add a second layer on top if necessary.
Drizzle the remaining olive oil and all of the lemon juice over the rolled dolmades. Pour in enough broth to just cover the top layer.
Place an inverted heat-proof plate directly on top of the dolmades to weigh them down, keeping them fully submerged and tightly rolled during cooking.
Bring the liquid to a gentle boil over medium heat. Reduce the heat to low, cover the pot with a lid, and let simmer for 40 to 45 minutes, or until the rice is tender and the meat is completely cooked.
Remove the pot from the heat and allow the dolmades to rest in the liquid for 10 to 15 minutes before serving. Serve warm with extra lemon wedges or traditional Avgolemono sauce.