In a large skillet heat oil over moderate heat until hot but not smoking and cook onions, stirring occasionally, until just softened. Remove skillet from heat and cool onions. With a sharp knife cut a slice from top and bottom of each melon to expose flesh and arrange with a cut side down on a cutting board. Cutting from top to bottom, remove rind. Halve melons, discarding seeds, and cut 1 cantaloupe half and 1 honeydew half into 1-inch-thick wedges. Arrange wedges in a platter. Cut remaining melon into 3/4-inch chunks and in a bowl toss with mint, lime juice, and pepper to taste.
Spoon melon mixture over melon wedges on platter and top with onions and pine nuts. Just before serving, toss mixture to combine.
(recipe courtesy of Gourmet Magazine)