This sauce is terrific on gingerbread, pumpkin pie, or apple crisp.
Without peeling or coring, chop into ¼-inch pieces:
Melt in a medium heavy saucepan:
Add the chopped apple and cook over medium heat, stirring occasionally, until softened, about 5 minutes. Add:
Simmer until the apple pieces are translucent, about 15 minutes. Transfer the apple mixture to a sieve set over a bowl. Return the liquid to the saucepan, then force the apple pulp through the sieve. Discard the skin and core. Stir the apple pulp into the liquid and boil rapidly over high heat, stirring, until reduced to about 1 cup. Remove from the heat and stir in:
When the butter is melted, if desired, add:
Serve at once, or let cool. Cover and refrigerate for up to 1 week. Reheat over low heat.