Cook the rice according to package directions. This will take about a half hour, or until the brown rice kernels soften and split. Drain and set aside.
Clean and dice the papaya. If using a mango, peel that, too, but if using peaches or apricots, you don’t have to remove the skin, which is tender and easy to eat.
Wash and spin dry the mesclun.
Juice one of the limes and whisk together with the olive oil, mustard, thyme and a generous pinch of sea salt.
Compose the salad: Place the greens on the bottom of a serving bowl. Add the rice, fruit and cucumbers. Cut the remaining lime into 6 wedges. Pour the dressing over the salad, toss and serve.