The order of the sautéing is the whole dish. Add water first and you get a clear soup; sauté in sesame oil and then add water and the broth turns cloudy and nutty, because the fat carries what comes out of the beef and radish and disperses it through the water.
Three or four minutes of sautéing makes the radish sweet. Heat collapses the cell walls and the sugars inside move into the broth. That is why it tastes sweet without any sugar.
Choose the section. The radish is sweetest at the top and most pungent at the tail — the pungent compounds (isothiocyanates) concentrate at the root tip. Use the middle for soup and the top for fresh salads.
Almost no vitamin C survives this soup. Raw radish holds 22 mg per 100 g, but it is heat-sensitive and 25 minutes of simmering takes much of it. If you want the vitamin C, eat radish raw or as kimchi. This soup's value is elsewhere: 400 g of radish adds only 72 kcal.
The 1.5 tbsp of soy sauce is nearly all the sodium here. Raw radish holds just 21 mg per 100 g. Drinking all the broth raises it, so sticking mostly to the solids is one option.
Skimming is about clarity rather than taste. The foam is coagulated protein from the beef — harmless, but it muddies the broth.
Use winter radish. Frost turns its starch to sugar and makes it far sweeter.