Preheat a sear nonstick 3-qt. sauté pan over medium heat. Add 1 Tbsp. olive oil and heat for about 1 minute.
Add cheese to the pan and sauté to crisp one side; turn over and crisp other side - about 1 minute per side.
To prepare the vinaigrette, add red wine vinegar to a small bowl. Slowly pour in 3 Tbsp. olive oil and whisk. Add green onions and season with salt and pepper.
Add the seared cheese and watermelon to the vinaigrette and toss to coat.
Set each piece of cheese in the center of a plate. Arrange the watermelon cubes on top of each piece of cheese. Spoon 1 tsp. of remaining vinaigrette over each serving.
Note: Prepared vinaigrette will also work for this recipe.