Buy firm or extra-firm tofu; softer varieties will fall apart on the grill.
Preheat grill to high (450°F to 550°F). Cut each tofu block in half lengthwise to make 4 (about 1-inch-thick) slabs. Wrap each slab in several layers of paper towels or kitchen towels. Let stand 10 minutes to drain excess liquid. Remove towels. Lightly brush tofu with grapeseed oil. Sprinkle 1 tablespoon of the brown sugar evenly over tofu. Sprinkle with pepper and 1/2 teaspoon of the salt.
Pulse cilantro, peanuts, olive oil, sesame oil, vinegar, garlic, chili, ginger, lime juice and remaining 1 tablespoon brown sugar and 1/2 teaspoon salt in a food processor until finely chopped.
Generously oil grill grate with grapeseed oil. Grill tofu until grill marks appear, 2 to 3 minutes per side. Cut each slab into 3 triangles. Serve with peanut sauce.