Brush each slice of watermelon with olive oil. In a grill pan or on the grill over medium-high heat, cook watermelon until char lines develop and watermelon lightly browns. About 3 minutes per side. Remove from grill and set aside.
On 4 separate plates arrange 1/4 cup arugula, grilled watermelon, feta, red onion, mint and basil.
Whisk together 1 tbsp. olive oil and balsamic vinegar. Combine and drizzle over plated salads.