Heat a panini press or gas grill to high.
Remove the each end of the watermelon. Stand the watermelon on either end and slice away the rind on each of the four sides, creating a solid rectangle of melon. Turn the block on its side and cut it into 6 squares, roughly 3-by-3 inches and 1-inch thick.
Toss the shallots with 1 teaspoon of olive oil and a pinch of salt. Grill the shallots for 2 to 3 minutes until softened and charred. Remove the grilled shallots to a small bowl and coat with the sherry vinegar.
Brush the watermelon in the remaining olive oil on each side. On a grill, cook until marked and warm, 5 to 7 minutes. On a panini press, cook for 10 to 12 minutes or until marked and warm.
Place the grilled square on a plate, top with the shallots, crumbled feta, olives and mint. Season with additional salt and pepper as desired.