Bring a large pot of water with a generous pinch of Salt (1 teaspoon) to a boil. While you wait for the water to boil, remove the core from the Green Cabbage (1 head).
Stick a fork into the center of the cabbage (where the core used to be) and dunk the cabbage into the boiling water until the outer leaves start to become soft. It should take about 3 minutes.
Remove the leaves from the pot as they become soft and continue this process until all of the leaves have been softened. Remove the thick portion of the main rib from each cabbage leaf with a knife and cut any especially large leaves in 1/2 if necessary.
Heat Olive Oil (2 tablespoon) over medium heat and cook the grated medium Onion (1) and Garlic (2 clove) for about 10 minutes, stirring often, until the onions soften and lightly caramelize.
Add Ground Beef (1 pound), Arborio Rice (1/2 cup), Fresh Dill (1/4 cup), Fresh Parsley (1/4 cup), Scallion (2), Salt (to taste), Ground Black Pepper (1/2 teaspoon), and the cooked onion and garlic together in a bowl, mixing until well combined.
Preheat the oven to 350 degrees F (180 degrees C).
Place a cabbage leaf on a work surface and add a generous tablespoon of filling, about the size of a walnut near the bottom of the leaf.
Fold the bottom end up over the filling, then fold the two side ends of the leaf inward and then roll the leaf into into a bundle making sure not to roll too tight as the filling will expand while it cooks.
Line a large baking crock with leftover cabbage leaves this is where we use up all of the small or torn leaves. This keeps the rolls on the bottom of the dish from over browning.
Arrange the cabbage rolls in the baking crock, packing them in rather snuggly so that they cannot move around while cooking and top the rolls off with more leftover cabbage leaves.
Add the Chicken Stock (3 cup) to the baking crock, cover and bake for 90 minutes.
In a heatproof bowl, set over a small pot of simmering water or use a double boiler add the Egg (4), juice from the Lemon (1), and Salt (to taste).
Whisk constantly until the sauce begins to thicken, the sauce is done when the whisk begins to leave a trail. Remove from the heat.
Spoon avgolemono sauce over the cabbage rolls and garnish with Fresh Dill (to taste).