How to Make It
Using a sharp knife, remove the skin from the prosciutto and cut it into 1-inch pieces. Cut the prosciutto meat and fat into 1-inch pieces and coarsely grind in a meat grinder or coarsely chop in a food processor, pulsing several times.
Transfer the ground prosciutto and the pieces of skin to a large soup pot. Add the carrot, onion, garlic, fennel seeds and rosemary and cook over moderate heat, stirring, until the fat is rendered, about 10 minutes. Add the cold water and bring to a boil. Simmer over moderately low heat until the broth is flavorful and reduced to 10 cups, about 1 1/2 hours. Strain the broth into a clean soup pot and refrigerate until chilled. Discard the solids.
Skim the fat from the broth and discard. In a medium bowl, knead the ground pork with the egg whites and lemon juice and stir it into the cold prosciutto broth. Slowly bring the broth to a simmer, stirring constantly until the pork mixture rises completely to the top. Stir gently to dislodge any pork from the bottom of the pot. Simmer over moderately low heat, undisturbed, for 15 minutes. Using a skimmer or a slotted spoon, gently remove the "raft" from the broth and discard.
Line a sieve with cheesecloth. Strain the consommé into a saucepan. Skim off any remaining fat from the surface. Season the consommé with salt and keep warm.
Place the melon balls and prosciutto ribbons in 4 shallow soup bowls and top with the arugula. Ladle 1 cup of the warm consommé into each bowl and serve.