Sauté the leeks, green garlic, carrot and kohlrabi stems in the olive oil. Add ½ tsp of salt to help draw out water from the aromatics. Sauté until everything is softened; expect about 5 minutes.
Add the kohlrabi to the pot and add enough stock to just reach the top of the ingredients. Turn the heat to high and bring to a boil. Lower the heat to low, cover the pot, and simmer.
After about 10 minutes, check on the status of the pot. It’s OK for the some of the kohlrabi to be above the level of the stock, but if it’s looking too dry, add more stock or just water.
Continue to check every 10 minutes. Adjust the liquid levels and check for doneness. Expect about 30 minutes to cook the kohlrabi to a soft and tender state. If you can easily push a wooden spatula through a chunk of kohlrabi, it’s ready for the next step.
Use an immersion blender to puree everything into a smooth soup. Before everything is totally smooth, make some final adjustments. First, taste for seasoning and mouthfeel. If the soup seems too thick, add stock or water. For a richer mouthfeel, add 2 ounces of cream. Add salt and pepper to taste. Finish the pureeing and serve hot.