Cut apples into quarters (removing the core & seeds).
Add the apples to a large stockpot with enough water to cover them by at least 2 inches.
Stir in maple syrup, brown sugar, ground cinnamon, ground allspice, and ground cloves.
Bring the mixture to a boil over medium-high heat. Boil, uncovered, for 1 hour.
Reduce the heat to low. Simmer (covered) for 2 hours.
Stain the mixture through a fine-mesh sieve. Discard the solids. Strain again through a sieve lined with a cheesecloth.
Add extra sugar if needed to sweeten to taste. Serve warm or cool.
