Pour 1 cup water into a small saucepan and add 3 to 4 cinnamon sticks, 1 tablespoon whole allspice berries, sliced ginger, and nutmeg.

Bring the mixture to a gentle simmer over medium heat and cook for 3 to 4 minutes until fragrant, without boiling vigorously.

Strain the spiced water through a fine mesh strainer into a large punch bowl, discarding solids, and allow it to cool for 5 minutes.

Stir in 1 cup packed brown sugar until fully dissolved, then add 1 teaspoon Angostura bitters and mix well.

Add 2 cups dark rum to the spiced sugar mixture and stir to combine.

Pour in 2 cups fresh orange juice, 1 cup fresh lime juice, and 1.5 cups pineapple juice, stirring until evenly blended; taste and adjust sweetness or acidity if desired.

Refrigerate the punch for at least 2 hours or up to 24 hours to chill and allow flavors to meld.

Serve punch over ice in glasses or a punch bowl, garnishing each serving with fresh orange slices and mint leaves.