HEAT THE OIL IN A STOCK POT over low heat, add the onions and cook slowly, stirring, about 7 minutes. Add the beets and continue to cook slowly, covered, until most of their water has been released and they have fallen apart, about 35 minutes. Stir often to avoid sticking and burning. Add the stock and salt, cover and bring to a boil. Reduce the heat and simmer, covered, for 15 minutes. When the soup is finished cooking, strain and reserve the liquid. Transfer the beets to a blender or food processor and add the watermelon. Puree until very smooth. Return the puree to the pot and add the reserved liquid. Chill the soup well, about 4 hours before serving.