Prepare the ingredients: thinly slice the Beef if not pre-sliced; core and chop the Napa Cabbage into bite-sized pieces; cut the Tofu into cubes; rinse and roughly chop the Shirataki Noodles; slice the Green Onion on the diagonal; trim stems and slice the caps of the Shiitake Mushrooms; trim the root end and separate clusters of the Enoki Mushrooms; and trim the Chrysanthemum Greens.
Make the sukiyaki sauce (warishita): in a bowl combine Soy Sauce, Mirin, Sake, Water and Sugar and stir until the sugar is dissolved. Taste and adjust balance of sweet and salty to your liking.
Heat a wide, shallow pot or heavy skillet over medium-high heat and add a little Beef Tallow to coat the bottom. When hot, quickly sear a few slices of Beef in a single layer until just browned; this renders flavorful fat and layers the pot with beef flavor.
Pour a portion of the prepared warishita into the pot to deglaze and bring to a gentle simmer — you want a shallow, flavorful broth rather than a full pot of soup.
Add the heartier vegetables and items that need more time first: scatter the chopped Napa Cabbage, the sliced Shiitake Mushrooms and the rinsed Shirataki Noodles into the simmering sauce. Tuck in the Tofu so it warms through and absorbs the broth.
Add the remaining uncooked Beef slices in folds or strips around the pot so each piece briefly poaches in the simmering sauce; cook only until just done (a few seconds to a minute, depending on thickness).
Finish with the quicker-cooking items: sprinkle the sliced Green Onion, arrange the Enoki Mushrooms and add the Chrysanthemum Greens on top; let them wilt for a minute or two in the simmering broth.
Taste the broth and adjust seasoning with more warishita or a pinch of Sugar if you want it sweeter. Keep the pot simmering gently while you eat so diners can continue adding and cooking ingredients at the table.
Serve family-style straight from the pot and offer small individual bowls of lightly beaten Eggs for dipping each bite — swirl a cooked morsel in the raw egg for a rich, velvety coating before eating.
