To prepare the ingredients, cut the onion half lengthwise into 4 wedges along the grain. Cut the carrot into bite-sized pieces and the celery root into 1-inch cubes. Thinly slice the beef and season with salt and pepper.
Slice the green beans into thirds. Bring a small pot of water to a boil and add a pinch of salt and add the green beans. Blanch them in the boiling water for 2-3 minutes and take them out, leaving the water in the pot.
Drain the shirataki noodles from the package and cut them in half. Blanch them in the boiling water you used earlier for 1 minute to get rid of any odor or flavor. Drain and set aside.
Heat the oil in a heavy-bottomed pot over medium heat. Add the sliced beef and let cook without stirring for 1-2 minutes until no longer red. Transfer 2 thirds of the meat to a plate, reserving a third in the pot.
Add the onions, celery, and carrots. Stir-fry for a couple of minutes until the celery cubes turn translucent. Add the dashi broth, cover with a lid, and bring to a boil.
Skim the foam from the surface. Add the soy sauce, mirin, sake, and erythritol. Add the shirataki noodles and stir.
Cover with a lid and simmer for 10-12 minutes over low heat, or until a skewer pierces the celery easily. Turn off the heat and remove the lid. Mix in the blanched green beans.
Let it stand uncovered for 30-45 minutes. This will intensify the flavors. Divide the stew into 4 bowls and serve immediately.