Step 1Place the peppercorns in a small skillet and dry-roast over medium-high heat, sliding the skillet back and forth over the burner to prevent burning, until the spice exudes a pleasant aroma, about 1 minute. Remove from the heat and transfer to a bowl to cool. Repeat with the coriander seeds. Grind the peppercorns and coriander seeds together and set aside.
Step 2Combine the garlic, peppercorns and coriander seeds, ginger, cayenne, salt, basil and soy sauce in a bowl and mix well. Add the oil and mix again to combine. Set aside. (Stored in a glass jar with a tight-fitting lid, the marinade will keep for a week in the refrigerator.)
Step 1Soak 16 to 18 bamboo skewers in water for 30 minutes, then pat dry.
Step 2Meanwhile, add the shrimp to the marinade and mix well to coat. Cover and refrigerate for at least 20 minutes, but no longer than 1 hour.
Step 3Mound the charcoal in one side of the grill, leaving the other side empty. Heat the grill.
Step 4Remove the shrimp from the refrigerator. Thread a shrimp from the tail through the body to the head onto a bamboo skewer, adding 3 to 4 shrimp to each skewer. Repeat with the remaining shrimp.
Step 5Spray the shrimp generously with vegetable oil. Lay the skewers with the shrimp portion on the grill over medium-high heat, arranging them very close to one another. (The uncovered portion of the skewers should not be over the coals.) Grill, turning frequently to prevent burning and brushing with the reserved marinade, until the shrimp are pink and firm, 3 to 4 minutes. Transfer to a platter and serve.