1. Make the spiced phyllo: Preheat oven to 400 degrees. Melt butter with cinnamon and ginger in a small saucepan. Cut 2 pieces of parchment to fit a rimmed baking sheet. Brush 1 piece of parchment with spiced butter, and sprinkle with 1 tablespoon confectioners' sugar. Place 1 phyllo sheet on top, and gently brush with spiced butter. Top with another phyllo sheet. Repeat, buttering and layering remaining sheets. Sprinkle remaining tablespoon confectioners' sugar on top. Using a paring knife, trim edges of phyllo to fit parchment, then cut into about 24 2-by-3 1/2-inch rectangles (don't cut through parchment).

2. Transfer parchment and phyllo to an upside-down rimmed baking sheet. Brush remaining sheet of parchment with spiced butter, and place on phyllo, buttered side down. Place another baking sheet, right side up, on top of phyllo. Bake until golden brown, 12 to 14 minutes. Transfer phyllo to a wire rack, and let cool. Phyllo will keep, covered, for up to 3 days.

3. Make the mint cream: Bring cream and mint to a boil in a small saucepan. Remove from heat, cover, and let stand for 1 hour. Prepare an ice-water bath. Strain cream into a bowl, discard mint, and stir in vanilla. Cover, and place bowl in ice-water bath. Let cool, stirring occasionally, about 20 minutes.

4. Make the mango filling: Combine all the ingredients in a bowl.

5. Make the mango caramel: Prepare another ice-water bath. Melt butter in a medium saucepan over medium-high heat. Add sugars, salt, ginger, and cinnamon. Cook, whisking constantly, until sugars begin to dissolve. Add lime juice, and cook, stirring often, until sugars dissolve and sauce thickens slightly. Stir in mangoes, bring to a simmer, and cook until mangoes are tender, about 15 minutes. Transfer to a bowl. Place bowl in ice-water bath, and let cool, stirring occasionally.

6. Place 2 tablespoons mango caramel in a medium bowl. Add mint cream, and whisk until soft peaks form.

7. To assemble: Place 1 phyllo rectangle on a plate, and spoon mango caramel over top. Top with mango filling. Using an offset spatula, spread 1 tablespoon whipped cream on top. Top with a second piece of phyllo, then caramel, filling, and cream. Dust a third piece of phyllo with confectioners sugar, then place on top. Repeat with remaining phyllo, caramel, filling, and cream. Garnish with mint sprigs, and serve.