Rinse the cranberries and pick out any soft or shriveled ones. Peel, core, and dice the apples into 0.5-inch pieces.
In a medium saucepan, combine the apple cider, granulated sugar, fine sea salt, and cinnamon stick. Bring to a simmer over medium heat, stirring until the sugar dissolves, 2–3 minutes.
Stir in the diced apples and simmer uncovered until they begin to soften but still hold their shape, 5–7 minutes.
Add the cranberries and cook at a gentle simmer, stirring occasionally, until most berries burst and the mixture looks glossy and thick, 10–12 minutes.
Remove from the heat and discard the cinnamon stick. Lightly mash a few berries with the back of a spoon if you prefer a less chunky texture.
Let the sauce cool at room temperature until it thickens further, about 15 minutes, then transfer to a container and chill until cold and set, at least 1 hour. Serve chilled or at room temperature.