1. Light a grill. In a bowl, combine the yogurt with the lemon juice, vinegar, thyme and the 1 tablespoon of olive oil. Season with salt and pepper.
2. Drizzle the watermelon triangles with olive oil and season with salt and pepper. Grill over high heat until nicely charred, about 1 minute per side; transfer to plates. Top the watermelon with the yogurt sauce and season with black pepper. Drizzle with olive oil, garnish with the mint and serve.