For filling, in a medium saucepan combine sugar, the water, and ginger. Bring to boiling over medium heat, stirring to dissolve sugar. Stir in figs. Boil gently, uncovered, for 12 minutes; remove from heat. Cover and let stand for 30 minutes.
Meanwhile, preheat oven to 350 degrees F. Grease twelve 2-1/2-inch muffin cups; set aside. Unfold phyllo dough; cover with plastic wrap. (As you work, keep the phyllo covered to prevent it from drying out; remove sheets as you need them.) Place one sheet of phyllo on a work surface; brush lightly with some of the melted butter. Top with a second sheet of phyllo. Repeat brushing and layering two more times (four sheets total). Brush top lightly with melted butter.
Cut phyllo stack in half lengthwise. Cut each half crosswise into three squares, making six squares. Repeat with the remaining phyllo sheets and butter to make 12 squares total. Gently press squares into prepared muffin cups, pleating as necessary to fit.
Bake for 10 minutes. Spoon filling evenly into phyllo cups. Bake for 5 to 10 minutes more or until phyllo is golden. Cool in muffin cups on a wire rack for 5 minutes. Remove from muffin cups; cool completely on wire rack. Before serving, top tarts with Honey-Mascarpone Cream. If desired, drizzle with honey.
In a medium bowl stir together mascarpone cheese and honey until smooth. In another medium bowl whisk whipping cream until soft peaks form (tips curl). Add one-third of the whipped cream to the mascarpone mixture. Stir until combined to lighten the cheese. Fold in the remaining whipped cream.