Rinse shrimp. Cut one pepper into rings, then mash with a mortar and pestle to form a paste. Cut oher pepper into thin strips.
Heat 2/3 cup coconut milk in a skillet over high heat. When it is almost boiling, spoon out 1 tablespoon and reserve. Reduce remaining cream for a few minutes until it's think and bubbly. Add curry paste and stir over med-high heat for a few minutes, until mixture is thick.
Increse heat to high and add remaining coconut milk, stirring well. Add sugar. Add shrimp and stir frequently for about 5 minutes.
Stir in crushed chilies and lime leaves. Stir about 30 seconds and then add basil leaves and strips of pepper. Stir well to wilt basil, then turn off heat.
Transfer to serving dish and dribble remaining coconut milk over top. Serve with rice.