Cut the bottom part of the watermelon to create a level base. Remove the rind into 1 1/2 to 2-inch wide slices, erring on the side of too wide. Cut the largest rectangle possible from each of these slices. You should be able to get about 6 good steaks from the watermelon. Pat dry each of the steaks with a paper towel, then place in refrigerator, uncovered, for 1 to 2 hours to dry out excess moisture. Give them a final pat dry right before cooking.
Heat 2 Tbsp of oil in a large skillet over medium high until almost smoking. Gently slide each steak in, cooking for about 3 to 5 minutes on each side until caramelized.
To serve:
Drizzle with balsamic reduction and top with basil & grated Parmesan.
Other options:
drizzle with honey, fresh mint, feta and toasted walnuts.