Toast sesame seed and shaved coconut in small skillet on medium heat about 30 seconds to 1 minute, just until lightly browned and fragrant. Remove from skillet and cool completely.
Place remaining ingredients in blender container. Blend on high until mostly smooth, about 2 to 3 minutes, scraping down sides of container frequently. Transfer to large pitcher. Stir in rum. Cover and refrigerate until chilled.
To serve, fill tiki-style beverage glasses with ice. Stir punch well and pour over ice in glasses. Sprinkle with toasted coconut mixture and top with mango. Garnish with lime wedges, if desired, and serve with a straw.
CHEF’s TIP
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For a little less ‘punch’, omit the rum and transform this tiki drink into a mocktail!
