PLACE water, cloves, cinnamon sticks and ginger in small saucepan; bring to a boil over medium heat. Remove from heat; cover. Cool for 15 minutes. Remove cinnamon sticks, cloves and ginger piece.
PLACE cream of coconut, evaporated milk, rum and cooled spice water in blender container; cover. Blend for about 30 seconds or until well blended. Refrigerate in glass container or bottle for at least 2 hours or until well chilled. Shake well before pouring.
TO SERVE: Serve in aperitif glasses for a 2-ounce serving. Sprinkle with cinnamon powder if desired.
Tip: Place a cinnamon stick in the bottled coquito for extra spice.
Recipe makes 5 cups.