How to Make It
In a small saucepan, combine the Scotch bonnet half with the onion, allspice, bay leaf, vinegar and sugar and bring to a boil. Remove from the heat, cover and let stand for 30 minutes. Strain the vinegar into a medium bowl and let cool.
Meanwhile, bring a medium saucepan of salted water to a boil and fill a bowl with ice water. Blanch the chayote and carrot in the boiling water just until crisp-tender, about 1 minute. Drain and transfer to the bowl of ice water. Drain and squeeze dry, then pat dry.
Add the chayote and carrot to the vinegar along with the parsley, lemon zest, lemon juice and mayonnaise and season with salt and pepper. Mince the remaining Scotch bonnet half and add it to the sauce.
Light a grill. Loosely thread the swordfish on 6 pairs of skewers. Thread the tomatoes on single skewers. Lightly brush the fish and tomatoes with oil and season with salt and pepper. Grill over moderately high heat, turning as necessary, until lightly charred and just cooked through, about 4 minutes for the tomatoes and 7 minutes for the swordfish. Transfer the skewers to a platter and pass the sauce at the table.