Wash and peel the skin off the ginger. Rinse the ginger. Grate or blend the peeled ginger in a blender or food processor. Grating the ginger is best, it brings out the flavor.
Place the ginger, lime juice, cinnamon stick, cloves and 3/4 cup of the sugar into a wide-mouthed gallon glass or ceramic jar.
In a large non-reactive (see notes) pot, add water, cinnamon, cloves, allspice, nutmeg and the lime peel, bring to a boil. Turn heat off and then add the raw sugar. Stir until the sugar is dissolved. Do a taste test, add more sweetener if desired. Mix in the fresh grated ginger and the juice from the lime.
Allow the ginger mixture to cool to room temperature. Cover and leave the mixture in the pot or pour it into a large jar with a lid. Refrigerate the ginger beer for at least 24 hours or up to a week. The longer it sits, the better the flavor.
When ready to serve, strain the beverage through a cheesecloth or fine colander. After the ginger beer is strained, press the solids to remove all liquid. Throw away the solids.
Serve cold. Garnish with lime wedges, fresh mint or a slice of ginger.
Reactive pots are made of aluminum, copper and cast iron. Non-reactive pots are said to be safe with all foods. A non-reactive pot refers to pots made out of glass, stainless steel, enameled cast iron or clay.