Place the quartered apples in a large stockpot. Pour in enough water so that, when the floating apples are gently pushed beneath the surface, they are covered by roughly 2 inches of water.

Add the packed light brown sugar, cinnamon sticks, and ground allspice. Stir until the sugar and spices are evenly incorporated throughout the mixture.

Set the uncovered stockpot over high heat and bring the apple mixture to a vigorous boil. Continue boiling for approximately 1 hour, stirring occasionally so the sugar dissolves thoroughly and the ingredients do not adhere to the bottom of the pot.

After the 1-hour boiling period, cover the stockpot with a lid and reduce the heat to low. Allow the mixture to simmer gently for 2 hours, checking periodically to ensure it maintains a quiet simmer without boiling over. During this stage, the apples should become very soft and the flavors will fully infuse the liquid.

Remove the pot from the heat and allow the cooked apple mixture to cool slightly so it is easier to handle.

Position a cheesecloth-lined strainer or a fine-mesh sieve over a large bowl. Carefully pour the apple mixture through the strainer, gently pressing the softened solids to release as much liquid as possible.

Discard the remaining apple solids. Pass the collected liquid through the cheesecloth or fine-mesh sieve once more to remove any remaining particles and produce a smoother, clearer cider.

Serve the finished homemade apple cider as desired.