Drain the ricotta overnight in the refrigerator in a sieve lined with cheesecloth or a coffee filter.
Place the ricotta in a food processor and pulse a few times until smooth.
Combine the balsamic vinegar and water in a saucepan. Cook over low heat until thick and syrupy, about 20 minutes. Add the honey and stir until dissolved. Remove from heat to cool.
To assemble, place a few spoonfuls of ricotta cheese on each plate and spread out the cheese, making a bed for the figs. Distribute the figs among the plates. Sprinkle with sea salt, drizzle with the balsamic syrup, and garnish with the mint leaves.