Remove peel from pineapples; cut peel into 3-inch pieces (reserve pulp for another use). Combine peels and 6 cups water in Dutch oven; bring to a boil. Reduce heat; simmer 30 minutes. Drain in a colander, reserving 4 cups cooking liquid; press peels to release moisture. Discard peels.
Combine ginger, lemongrass, and 2 tablespoons water in a food processor; process until finely chopped. Place ginger mixture on a dampened double layer of cheesecloth. Gather edges of cheesecloth together; tie securely. Place cheesecloth bag and 4 cups water in a medium bowl; let stand 30 minutes. Strain reserved pineapple cooking liquid and ginger mixture into a large pitcher; discard cheesecloth bag. Add sugar; stir well. Chill. Serve over ice. Garnish with mint sprigs, if desired.
I make this all the time when I've got fresh pineapple trimmings - but make it even easier: put the trimmings, minced ginger, juice and rind of 1 lemon, plus mint sprigs (lots) in large soup pot with water.....boil all and simmer 30. Strain - add sugar if desired. Pour into empty water gallon jug. Chill. Perfect to cart to picnics and baseball games, etc.
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