Place all the ingredients in the bowl of a food processor. Pulse until smooth.
Place a grill pan over medium-high heat or preheat a gas or charcoal grill. Cut the tofu in half diagonally to make 2 large triangles. Cut each large triangle in half to make 4 smaller triangles. Place the triangles, long side down, on a cutting board and carefully cut each into 3 slices. Brush the tofu triangles, on each side, with the extra-virgin olive oil. Season with salt and pepper. Grill the tofu for 2 minutes on each side.
Carefully transfer the tofu to a serving platter. Spoon the pesto over the tofu and serve.