Halve and seed the honeydew melons. Cut 2 (1/4-inch) slices from each honeydew melon half. Shape the honeydew slices to look like the egg white of a sunny-side-up egg. Slice the cantaloupe in half and use a melon scoop or a measuring tablespoon to carve out 4 "yolks".
Trim the melon balls to resemble yolks. Assemble "eggs" and position 2 strips of prosciutto "bacon" alongside them. Garnish with parsley and serve immediately, or refrigerate. For the best contrast, use solid-color plates that are neither white nor yellow.