Place all of the ingredients in a medium saucepan. (Wine should come halfway up sides of chorizo.) Bring to a boil over medium-high heat. Reduce heat, and simmer, flipping chorizo once, until sausage is tender and liquid has been reduced by half, about 20 minutes. Discard oregano sprigs.
Cut chorizo diagonally into 1/4-inch-thick slices, and arrange on plates. Drizzle with braising liquid, and garnish with additional oregano sprigs.