Combine the cider, sugar, apple, allspice berries, peppercorns and 1/2 teaspoon salt in a medium saucepan over medium-high heat. Bring to a boil and cook, stirring once, until the apple starts to fall apart and the liquid is syrupy, 20 to 25 minutes.
Add the cranberries and cook, stirring and skimming the foam off the top until the berries burst, 6 to 8 minutes. Let cool slightly, then transfer to a blender and puree until almost smooth.
Strain through a medium-mesh sieve into a bowl, pressing on the solids; smooth the top. Let cool 30 minutes, then cover and refrigerate until set, at least 2 hours.
Make the sauce up to 1 week ahead; cover and refrigerate.