1Place cranberries, 1/4 cup of the water, and the brown sugar in a large bowl and mash with a potato masher until the cranberries are completely smashed and the brown sugar has dissolved slightly.
2Add the remaining 1 1/4 cups water, apple cider or juice, brandy, lemon juice, and maple syrup and stir vigorously until well combined and the sugar has completely dissolved. Pour the mixture through a strainer set over a 10-cup pitcher and discard the solids left in the strainer. Chill for at least 1 hour, or until cold.
3If desired, transfer the mixture to a punch bowl and top with apple slices. To serve, pour 3 ounces of the punch into a highball glass filled with ice. Garnish with a thin slice of apple.
In this episode of CHOW Happy Hour, Martin Cate, of Smuggler's Cove in San Francisco, explains the culture of the Ti Punch from Martinique. If you order it on the Caribbean island, you might actually be in charge of making your cocktail yourself!