Place 2 cups arugula, ½ cup basil, Parmesan cheese, pine nuts, and garlic in a food processor or blender. Cover and process or blend until finely chopped. With the motor running, gradually add olive oil until well combined. Stir in salt and pepper.

Combine tomatoes, mozzarella, and onion in a medium bowl. Add 2 tablespoon arugula pesto; gently stir to combine.

Heat a grill pan over medium-high heat. Spray asparagus with nonstick spray. Grill 6 to 8 minutes or until crisp-tender, turning occasionally.

Arrange asparagus on a serving platter. Spoon tomato mixture over asparagus. Garnish with additional basil leaves and fresh arugula, if desired. Serve with remaining arugula pesto.