First, start a large quantity of water, to cook the noodles, in a deep pot.
In a skillet, heat the cooking oil, then add the ginger, lemongrass and garlic, and sauté for 1 minute, stirring quickly. Add the ground beef and sauté it, breaking it up into grains, until it loses its color.
Add the whole bean sauce and the chili paste. Stir everything together. Add the sugar and the water, and stir again. Add the eggplant coins, and bring the liquid to a simmer. The water should not be covering the eggplants—they should be sitting in it with the liquid level about a third of the way up their sides.
Cover the pan. Cook on a gentle simmer for about 6 or 7 minutes.
When the pot of water boils, add the Chinese egg noodles. Stir to make sure the noodles do not stick together, bring back to a boil, then reduce the heat to simmer and cook until al dente.
Back to the meat sauce. Uncover the pan and raise the heat—you want to cook the liquid down until there is a small amount in the bottom of the pan—a coating on the bottom. At this point, stir in most of the scallions, reserving about a teaspoon for garnish, and stir in the sesame oil. If the noodles are not cooked yet, turn off the heat and cover the pan.
When the noodles are cooked, drain them. We served this by plating the noodles and then topping with the sauce and then the scallion garnish, but you may prefer to mix everything together in a big bowl and pass the bowl, family style.