Preheat the grill to medium-high heat (425 °F).

Cut 8 pieces of watermelon into triangles for garnish, about ½ inch thick. Brush the triangle garnishes with olive oil and place the brushed side down on the grill. Cook for 1-2 minutes, or until slightly charred. Remove with tongs and allow to cool.

Peel the remainder of the ½ watermelon and blend in a food processor or blender until smooth. Add the aperol, lemon juice and salt and pulse for 1 minute. Strain the watermelon mixture and add to a pitcher with the seltzer and ice.

Pour into glasses and garnish with the grilled watermelon.