Thourougly rince any grit from the radish leaves. The easiest way to do this is with a salad spinner. Place the leaves in the spinner basket inside the spinner bowl and fill with water. Swirl the leaves in the water and pull the basket from the water. Check for any grit in the bottom of the bowl. Dump the water and repeat until no grit appears at the bottom of the bowl.
If using potatoes, peel them and cut the flesh into 1 inch pieces. If using radishes, optionally peel them, and if necessary cut them into 1 inch pieces.
Sauté the onions in olive oil with ½ tsp of salt in the soup pot. Use enough olive oil to make the onions glisten, but not enough to pool in the bottom of the pan. You just want to sweat the onions, with no browning. When they are soft and translucent, stir in the garlic and sauté another minute or two.
Add the radish leaves and either potatoes or radish roots to the pot and add enough stock to just reach the top of the other 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. If there appears to be excess liquid, let the simmering continue without the cover. If most of the ingredients are above the stock line, add more stock. Once the liquid level looks right, cover and continue simmering.
Continue to check every 10 minutes, adjusting the liquid levels. When the potatoes or radish roots are soft, expect about 30 minutes into the simmering, everything is fully cooked.
Once the ingredients are fully cooked, use an immersion blender to puree everything into a smooth soup. Final adjustments are made at this time. If the soup seems too thick, add stock or water. Taste for seasoning and creaminess. For a richer mouthfeel, add cream at this point. Add salt and pepper and other seasonings to taste.