Use a sharp knife or a vegetable peeler to remove the zest from the oranges in strips, being careful to remove only the orange part, leaving the pith behind. Then, juice the oranges into a large, heavy-bottomed pot.

Pour the red wine and white wine into the pot with the orange juice. Place the strips of orange zest, ginger, cinnamon sticks, cloves, and brown sugar into the pot with the wine mixture; stir to dissolve the sugar.

Cover and heat over medium-high until heated through, but not boiling, reduce the heat to medium-low and heat for an hour or longer to bring all of the flavors together. Adjust the sweetness by adding more brown sugar, as necessary. Strain and serve hot with a splash of brandy, if desired.