For the marinade:
24 jumbo shrimp (1-1½ pounds), shelled and deveined
2 tablespoons vegetable oil
1 tablespoon fresh lemon or lime juice
1 garlic clove, minced
Salt and freshly ground black pepper
For the glaze:
½ cup dark brown sugar
1 stick (8 tablespoons) unsalted butter, cut into 1-inch pieces
½ cup dark rum
3 tablespoons Dijon mustard
1 tablespoon white vinegar
¼ teaspoon cinnamon
¼ teaspoon ground cloves
¼ teaspoon black pepper
Pinch of salt
1 package sugar cane swizzle sticks (optional)
Vegetable oil, for the grill
In a large mixing bowl, stir together the oil, lemon juice, garlic and salt and pepper to taste. Add the shrimp and toss to coat. Allow to sit for 15 minutes while preparing the glaze.
In a medium saucepan, combine the brown sugar, butter, rum, mustard, vinegar, cinnamon, cloves, pepper and salt. Bring to a boil, then reduce heat to medium. Simmer the mixture, stirring occasionally, until thick and syrupy, 5 to 8 minutes. Taste for seasoning and adjust as needed.
Remove from heat and set aside. Cut the sugar cane crosswise on the diagonal into 5-inch sections, then halve each section lengthwise. You can prepare the recipe several hours in advance up to this step.
Set up your grill for direct grilling. Using a bamboo skewer, make two starter holes in each shrimp. Skewer the shrimp with the sugar cane. Brush the grill grate with oil. Grill the shrimp until cooked through, 2 to 3 minutes per side, generously basting with the glaze. Serve additional glaze alongside.