1/4 cup freshly squeezed lime juice, plus 1 tablespoon (3 limes)
1/4 cup dark rum
3 tablespoons dark-brown sugar
1 tablespoon finely grated, peeled fresh ginger
1 1/2 teaspoons cornstarch
32 medium shrimp, peeled and deveined (tail on)
Coarse salt and ground pepper
1 ripe but firm mango, peeled and sliced lengthwise into 8 slivers, each about 1 inch thick
2 tablespoons vegetable oil, plus more for grates
2 bunches watercress, (about 12 ounces), tough stems trimmed
Make glaze: In a small saucepan, combine 1/4 cup lime juice, rum, sugar, and ginger; bring to a boil over high heat. Reduce heat; simmer, whisking occasionally, until slightly thickened, about 3 minutes. In a small bowl, whisk together cornstarch and 1 tablespoon water; stir into lime-juice mixture. Cook, stirring, until thickened, about 30 seconds. Remove from heat; let cool.
Thread shrimp onto 8 skewers, using 4 shrimp per skewer. Season on both sides with salt and pepper. Thread mango slivers onto 4 skewers, using 2 pieces per skewer. Brush shrimp and mango all over with glaze.
Heat grill to medium-high; oil grates. Place shrimp and mango skewers on grill; cook, turning once, until blackened in spots and shrimp are opaque throughout, 3 to 4 minutes.
In a large bowl, whisk together remaining tablespoon lime juice with the oil; season with salt and pepper. Add watercress; toss to coat.
To serve, divide watercress among four plates; top each with 2 shrimp skewers and 1 mango skewer.