Combine liquid and sugar: In a medium saucepan, stir together the orange juice, sugar, orange zest, cinnamon stick and salt. Place over medium-high heat.

Dissolve the sugar: Bring the mixture to a boil, stirring often, until the sugar fully dissolves into the juice, about 2 minutes.

Add the cranberries: Stir in the fresh cranberries and the ginger, if using. Return the pot to a boil.

Lower to a simmer: Reduce the heat to medium-low so the mixture bubbles gently rather than boils hard. A hard boil can scorch the sugar on the bottom of the pan.

Listen for popping: Cook uncovered, stirring occasionally, and listen for a soft crackling sound as the cranberry skins start to split, about 5 minutes in.

Simmer until thickened: Continue cooking until most of the berries have burst and the liquid turns glossy and darker, about 10 to 12 minutes total.

Check the consistency: The sauce should coat the back of a spoon in a thin, syrupy layer; it will thicken more as it cools, so don't overcook it looking for a thick sauce in the pot.

Remove the cinnamon stick: Take the pan off the heat and fish out the cinnamon stick with a fork or tongs.

Cool before serving: Let the sauce cool at room temperature for about 30 minutes, then transfer it to a serving bowl or airtight container and refrigerate until ready to serve.