Combine first 5 ingredients in a large saucepan; bring to a boil. Add figs. Reduce heat; simmer 2 minutes. Remove figs with a slotted spoon, and place in a shallow dish. Cover and chill. Bring the cooking liquid to a boil, and cook for 15 minutes or until reduced to 1/2 cup. Cover and chill.
Preheat oven to 450°.
Roll dough into a 12-inch circle on a lightly floured surface; cut dough into 8 (4-inch) circles, rerolling dough scraps as necessary. Fit each dough circle into a 3 1/2-inch tart pan. Bake at 450° for 7 minutes or until lightly browned. Cool completely on a wire rack.
Combine ricotta and honey. Spread about 1 1/2 tablespoons ricotta mixture into each tart shell. Arrange 3 fig halves, cut sides up, inside each shell. Drizzle each tart with 1 tablespoon of the wine mixture. Garnish with mint, if desired.