First, prepare the dressing.
In a screw-top jar or small bowl, combine the 2 to 3 tablespoons (45 ml / 1.5 fl oz) of olive oil, lemon juice, red wine vinegar, salt, and pepper.
Cover and shake vigorously until well combined.
Set aside.
Place the arugula in a medium bowl. Just before serving, shake the dressing again and drizzle it over the arugula, tossing gently to coat every leaf.
Prepare your grill for direct, medium heat.
Brush both sides of the flatbread with the 2 teaspoons (10 ml / 0.3 fl oz) of olive oil.
Grill for 1 to 2 minutes per side, or until golden brown with beautiful grill marks.
Transfer the warm flatbread to a cutting board.
Spread it evenly with the pesto or tapenade.
Top with the dressed arugula, sliced olives, and a generous sprinkle of shaved Parmesan cheese.
Slice and serve immediately.