Slice the cabbage in half through the core, then cut each half into two wedges (you’ll have 4 wedges total). Place them on a baking sheet or roasting pan.
Drizzle the wedges with olive oil and sprinkle with salt, coating each side evenly. Roast for 45 minutes, flipping once halfway through, until the cabbage is tender with crispy, slightly charred edges.
While the cabbage roasts, whisk together the peanut butter, water, lime juice, soy sauce, ginger, garlic, and smoked paprika (if using) in a small bowl or jug until smooth and creamy.
Plate the roasted cabbage and drizzle generously with peanut sauce. Garnish with fresh cilantro, if desired. Serve warm as a side or over noodles, rice, or salad bowls.