In a large stockpot, combine diced apples, water, and butter. Cook over low heat, stirring frequently, until apples are tender (about 10 minutes).
Stir in pectin, then bring the mixture to a rolling boil while stirring constantly.
Add granulated sugar, brown sugar, cinnamon, and nutmeg, then return to a rolling boil. Stir constantly for 1 minute.
Remove from heat, skimming any foam. Ladle the hot jam into hot, sterilized jars, leaving 1/4-inch headspace.
Remove any air bubbles, wipe rims, and adjust lids. Process jars in a boiling water bath for 10 minutes.
Twist jars gently from side to side while cooling to evenly distribute apple pieces throughout the jam.