For the Tofu:
Place a griddle pan over medium-high heat or preheat a gas or charcoal griddle. Cut the tofu in half diagonally to make two large triangles. Cut each large triangle in half to make four smaller triangles.
Place the triangles, long side down, on a cutting board and carefully cut each into three slices. Brush the tofu triangles, on each side, with the extra-virgin olive oil. Season with salt and pepper. Cook the tofu for two minutes on each side.
Carefully transfer the tofu to a serving platter. Spoon the pesto over the tofu and serve.