Place first 5 ingredients in a small saucepan over low heat. Simmer 15 minutes, stirring often. Remove from heat. Remove ginger with a slotted spoon and discard. Allow mixture to cool.
Place 1 tablespoon each sesame oil and peanut oil in a heavy saucepan over medium-high heat until hot. Add onion and cook, stirring constantly until onion is transparent. Add rice, stirring well. Add water and bring to a boil. Reduce heat to low and simmer uncovered for 15 minutes. Cover; cook 3 minutes, stirring occasionally.
Whisk egg in a large bowl and mix in cooled coconut milk mixture. Stir in mint, cilantro, garlic, green onion, red pepper, salt and black pepper. Add rice mixture, stirring until combined. Stir in flour, mixing well. Set aside. (Mixture may be refrigerated at this point for a few hours before cooking if desired.)
Thread shrimp onto skewers. Coat grill rack with cooking spray. Grill shrimp on rack over medium-hot coals, covered, 3 to 4 minutes on each side or until shrimp turn pink. Remove shrimp from skewers. Keep warm.
Heat 2 teaspoons peanut oil in a large heavy skillet over medium-high heat. Fill in a ¼-cup dry measuring cup with rice mixture just until it holds its shape. Carefully remove shaped rice mixture from cup and place in hot skillet. Press gently with back of a spatula until cake is about ½-inch thick. Repeat procedure with remaining rice mixture. Cook rice cakes 2 to 3 minutes on each side or until lightly browned. Remove from skillet.
To serve, place 2 cakes on individual serving plates. Top each serving with 8 grilled shrimp. Drizzle sauces on top.