This recipe from Maya at My Feasts creates a pretty close approximation of the soup I had that day. First, sautée leeks, ginger, and garlic over medium-low heat, and then add roasted beets, salt, pepper, and broth to the pot. After allowing the ingredients to simmer for a bit, purée, then finish with fresh lemon juice. It's a simple recipe, with great results. Not only does the soup have a nice ginger-beet flavor, but it will make your kitchen smell wonderful.
My only stray from the recipe was using water in place of broth -- happily, the leeks, garlic, ginger, and beets created their own.