Walnuts can be made up to 3 days in advance. Store in an airtight container in a cool place.
2. In a medium skillet, combine sugar, 2 tablespoons water, oil, and cayenne pepper. Bring to a boil, reduce heat to medium, and stir in walnuts. Cook about 5 minutes, stirring occasionally, until sugar caramelizes and coats nuts.
3. Spread nuts on a parchment-lined baking sheet, breaking apart clumps while still hot; cool completely.
4. Remove stems and slice figs in half lengthwise. Arrange groupings of figs, cheese, walnuts, and crackers on a wooden board or platter. Encourage guests to combine ingredients on crackers.