Slice the watermelon into triangles; set the triangles in a colander to drain while you prepare the rest of the salad.
Combine the olive oil, lime juice, and vinegar in a small glass jar with a tight-fitting lid.
Preheat a grill (or frying pan) to medium-high heat. Brush the cheese lightly with avocado oil on both sides.
Arrange the watermelon on a serving platter.
Place the cheese on the grill and cook for 2–4 minutes per side, or until grill marks develop and the cheese begins to melt. Cut the slices into large pieces.
Arrange the cheese on the platter with the watermelon, sprinkle with mint, and pour the dressing over the salad.
Serve immediately, while the cheese is warm.