Slice the avocados lengthwise into 1/2-inch thick slices. Slice the papayas widthwise into 1/2-inch thick slices. Arrange overlapping slices on a serving platter, alternating slices of avocado and papaya.
In a small bowl, combine the remaining ingredients and stir to combine. Spoon the dressing over the avocado and papaya. Serve immediately.