In a 2-cup container, COMBINE the milk, peel, juice, sugar, paste, sauce and ginger; STIR well; SET aside.
PREPARE shrimp; PLACE in a medium bowl; POUR 1/2 cup of the milk mixture over shrimp; COVER shrimp; REFRIGERATE for 30 minutes.
Meanwhile, start rice COOKING according to recipe.
DRAIN shrimp, discarding marinade; THREAD shrimp onto skewers (do 4 to 5 shrimp per skewer), leaving 1/4-in between pieces.
GRILL over medium heat, turning once, until shrimp are opaque and pink, about 4 to 5 minutes per side.
Meanwhile, HEAT reserved coconut mixture until boiling; REDUCE heat; SIMMER, uncovered, for 5 minutes.
Place grilled shrimp on bed of hot rice; ladle on hot coconut mixture.
Per Serving (excluding unknown items): 88 Calories; 8g Fat (76.1% calories from fat); 1g Protein; 4g Carbohydrate; trace Dietary Fiber; 1mg Cholesterol; 67mg Sodium. Exchanges: 0 Grain(Starch); 0 Lean Meat; 0 Vegetable; 0 Fruit; 4 1/2 Fat; 0 Other Carbohydrates.