Put broth and water in a large soup pot and heat to a boil over medium-high heat. While broth is heating, prepare fennel and onion. Cut tops off fennel, reserving a few of the best fronds. Add vegetables to broth along with garlic, bay leaves, dill, and salt & pepper (to taste). Bring to a boil, reduce heat, cover, and simmer about 15 minutes or until vegetables are cooked.
Remove bay leaves and discard. Purée soup (use a blender, food processor or immersion blender) to a smooth consistency. Return to pot and swirl in the 1/2 cup potato flakes. Add chopped fronds. Remove pot from heat.
Core unpeeled apple and chop into a fine dice. Ladle soup into four bowl. Top each with 1 tbsp apple and 1 tbsp cheese.