In a 6- to 8-quart heavy pot combine the the first four ingredients (through lemon juice). In a small bowl stir together 1/4 cup of the granulated sugar, the apple pie spice, and pectin. Stir into apple mixture. Bring to a full rolling boil, stirring constantly. Stir in the remaining 3/4 cup granulated sugar and the brown sugar. Return to a full rolling boil, stirring constantly. Boil hard 1 minute, stirring constantly. Remove from heat. Quickly skim off any foam with a metal spoon.
Ladle hot preserves into hot, sterilized half-pint canning jars, leaving a 1/4-inch headspace. Wipe jar rims; adjust lids and screw bands.
Process filled jars in a boiling-water canner 10 minutes (start timing when water returns to boiling). Remove jars from canner; cool on wire racks.