For the soup
Place the melon, fennel, orange juice, buttermilk, garlic, vinegar, salt and pink pepper in a blender and blend until the ingredients become a smooth, velvety purée.
Pour the purée to a bowl, stir in the chopped basil and refrigerate.
For the feta bites
Dust the feta cheese cubes with flour, dip into the beaten eggs and coat with sesame seeds. Repeat until all cubes are coated.
Heat the oil in a large skillet. Fry the coated feta cubes for 1-2 minutes on each side.
Divide the soup into 6 bowls and place 4 feta bites into each bowl. Sprinkle with grated carrot, pink pepper and basil leaves. Drizzle with olive oil and serve.