Preheat oven to 350ºF. Put figs, cider, orange juice, lemon juice, cinnamon stick, star anise, lemon peel, thyme, ground cloves and salt in medium pot. Bring to a simmer over medium heat. Reduce the heat to low and continue to simmer for about 30 minutes, until thickened and syrupy. Remove and discard cinnamon stick, star anise, lemon peel and thyme stems. Let cool to room temperature.
Arrange baguette slices on a large rimmed baking sheets; brush both sides with oil. Bake until lightly golden, 10 to 12 minutes. If undersides are not browning, turn crostini over once during baking. Remove from oven and let cool on baking sheets. Spread ricotta on crostini, then place a spoonful of compote on top. Drizzle with liquid from compote. Store extra compote in a covered container in the refrigerator for up to 2 weeks.