In a large blender add all the ginger and 5 cups of hot water. Blend very well and strain the liquid from the pulp into a large bowl. Squeeze the pulp until you have gotten all the liquid out.
Place the pulp back into the blender and repeat the steps above with the remaining 5 cups of hot water.
Add the cloves and let the liquid steep for at least 4 our to overnight in the fridge.
Line your strainer with cheesecloth and strain again into another bowl. Then add the lime juice, brown sugar (to taste) and the optional rum. Stir until all of the sugar has dissolved.
Serve in a glass that is filled with ice. Keep the rest in large bottles and store in fridge.