For the tofu: Place a nonstick grill pan over medium-high heat or preheat a gas or charcoal grill. (If not using a nonstick grill pan, oil the grill lightly before cooking the tofu to prevent sticking.)
Cut the tofu in half diagonally to make 2 large triangles. Cut each large triangle in half to make 4 smaller triangles. Cut through each triangle horizontally to make 8 triangles. Brush on each side with olive oil. Season with the herbs de Provence, salt and pepper. Grill the tofu until light golden, 2 minutes on each side. Transfer to a platter.
For the cream: In a food processor, blend the avocado, parsley, broth, olive oil, lime juice, garlic and lime zest until smooth. Season with salt and pepper.