1. Heat oven to 400° F. Roast yams until soft (1 hour, or microwave until soft, 10 minutes).
2. Scrape out flesh; discard the skin. Purée flesh in a food processor with 2 1/2 TBSP olive oil, warm water, grated cheese, ginger, cumin, salt, and pepper.
3. To serve: Drizzle with remaining olive oil and garnish with sea salt.