Fill a tall, 8-quart (or larger) pot with enough water to submerge the whole cabbage and bring to a boil over high heat. Boil the cabbage until the outer leaves are bright green and start to pull away, about 4 minutes. Carefully pull them off with tongs and lay them on a baking sheet lined with a kitchen towel. Continue boiling the cabbage and removing its leaves in layers as they soften until the entire cabbage is cooked, 15 to 20 minutes total. Let cool.
In a large bowl, use your hands to combine the lamb, onion, egg, feta, rice, parsley, oregano, lemon juice, cumin, fennel, 2-1/2 tsp. salt, and 1 tsp. pepper.
With a paring knife, remove the hard ribs from the cabbage leaves. Cut the larger leaves in half lengthwise.
Coat the bottom of an 8- to 9-quart Dutch oven with the olive oil. Arrange several cabbage leaves on a work surface so they run lengthwise away from you. Working with one leaf, put about 1-1/2 Tbs. of the lamb mixture on the end closest to you. Fold the long sides in toward the lamb, and then roll away from you to enclose the meat. Put the roll in the pot, seam side down. Repeat with the remaining cabbage and filling, arranging the rolls in a snug single layer (if necessary, add a loosely packed second layer).
Combine the tomatoes, broth, and ouzo in a medium bowl and pour the mixture over the rolls. Bring to a boil over medium heat. Reduce to a gentle simmer, cover, and cook, shaking the pot occasionally so the rolls don’t stick, until the rice in the filling is completely tender, 60 to 90 minutes.