Start by making the pickled onions. Finely slice the onions and place in a container. Put the vinegar, 200ml water, sugar and salt in a saucepan and bring to a simmer. When the sugar and salt has dissolved, pour the mixture over the onions and place in the fridge overnight.
Preheat the oven to 180 degrees. Slice the beetroot into chunks. Peel the onions and cut them into chunks too. Put on a baking tray and drizzle with olive oil. Roast for 30 minutes.
Tip the beetroot and onion from the baking tray into a large saucepan. Pour over the stock then bring to a simmer and cook for 20 minutes. The beetroot should be soft if you stick a knife into it.
Turn off the heat, then blend with a stick blender until smooth. Taste, season with salt and pepper as needed, then put in the fridge to chill (for at least 2 hours).
When you are ready to serve, ladle the soup into bowls and top with finely sliced radish, finely chopped pickled onion, sprigs of dill, crumbled feta and edible flowers.