If using a gas grill, preheat grill for 5-10 minutes before cooking the shrimp--there is usually enough time to do this while preparing the shrimp. If using charcoal, start it early enough to make sure coals are hot and glowing before cooking shrimp.
For the sauce: Combine the honey, rice vinegar, fish sauce, sherry, chili garlic sauce, garlic, and dissolved cornstarch in a small sauce pan and stir to combine over medium heat. Cook until sauce begins to bubble and thickens, about 5 minutes. Remove from heat and set aside.
Squeeze the juice from one of the lime halves into the melted butter, stir to combine. Once the shrimp are peeled and deveined (leave the tails on), place in a bowl and squeeze the juice from the other half of the lime over the shrimp and toss.
Place the shrimp on skewers so the skewer goes through part of the end by the tail and part of the thicker end to form a crescent shape. Line the shrimp on the skewer one after the other without smashing the shrimp together or crowding.
Once the grill is ready and the sauce is made, brush the shrimp with lime-butter on both sides.
Grill over medium-high heat about 2-3 minutes on each side, brushing more butter on after turning, until the shrimp turns from grey to bright pink in color and the flesh appears opaque. Brush each side with sauce and grill for 1 minute.
Remove from the grill and sprinkle with sesame seeds. Serve with lime wedges and additional sauce at the table. Squeeze lime juice over the shrimp just before eating.
Larger, meaty shrimp 10-16 count are an excellent choice for the grill, using a fish basket or skewers work best for containment.
Add more honey for a sweeter sauce, dried chili peppers to kick up the heat, or vinegar and lime for more tangy bite.