Combine shrimp, olive oil, and jerk seasoning in a large bowl; allow to sit for 15 minutes.
Skewer shrimp onto metal or wooden skewers and then grill until cooked through but not overdone.
Sweet Green Tomato:
Dice the green tomato into very small pieces, and then toss with the granulated sugar and sea salt in a small bowl.
Allow to sit for 15 minutes and then drain off any liquid.
Cut eggs in half lengthwise and place the yolks in a food processor.
Add the mayonnaise and mustard and then puree until extremely smooth.
Place the egg mixture into a large Ziploc bag, snip off the end, and then pipe the filling into the eggs.
Place a shrimp on top of each deviled egg and then garnish with sweet green tomato.