How to Make It
In a small saucepan, combine the butter with the parsley, basil, garlic and shallot and melt over low heat.;
Light a grill or heat a grill pan. Halve the shrimp lengthwise, leaving them attached 1 inch below the head. Devein the shrimp and spread them open. Season with salt and pepper, then brush liberally with the herb butter.
Grill the shrimp over a medium-hot fire, shell side down, until lightly charred, about 1 minute. Turn and grill the other side until lightly browned, about 40 seconds. Turn the shrimp again. Brush them liberally with more herb butter, sprinkle with rum and grill until barely cooked through and bubbling, about 1 minute longer. Serve at once.