1. Put cinnamon, star anise, cloves, and peppercorns in a heavy plastic food bag; coarsely crush with a rolling pin.
2. Trim and discard root ends and coarse outer leaves from lemon grass. Chop tender white part of stalks.
3. In a 1- to 1 1/2-quart pan over high heat, combine 2 cups water, crushed spices, lemon grass, 2/3 cup sugar, orange peel, and ginger. Slit vanilla bean lengthwise; scrape seeds into pan and add pod. Bring to a boil, remove from heat, cover, and let stand at least 1 hour.
4. Pour spice syrup through a fine strainer into a bowl; discard residue. Add rum, cover, and chill until cold, at least 2 hours or up to 2 days.
5. Meanwhile, in a bowl with a mixer on high speed, whip egg white until it holds soft peaks. Gradually add remaining 1/3 cup sugar, and continue to beat until white holds distinct peaks. Fold in coconut.
6. Line a 12- by 15-inch baking sheet with cooking paper or parchment. With a narrow spatula, spread egg white mixture in a 10- by 13-inch rectangle.
7. Bake in a 350° oven until meringue is deep golden brown, about 10 minutes. Let cool on sheet to room temperature. Gently pull off paper, then break meringue into 4 or 8 equal pieces.
8. Spoon fruit equally into wide soup bowls and fill equally with spice syrup. Scoop sorbet into balls and add equally to bowls; insert meringue pieces into sorbet, and garnish with mint sprigs.
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