Oyster-Cornbread Stuffing

Ingredients

• ["2 cups low-salt chicken broth", "1 sprig sage plus 1 tablespoon thinly sliced sage leaves", "1 sprig rosemary", "1 pound breakfast sausage, casings removed", "1/4 cup (1/2 stick) unsalted butter", "2 medium onions, finely chopped", "1 1/2 cups finely chopped celery", "1/4 cup finely chopped flat-leaf parsley", "2 tablespoons finely chopped fresh thyme", "Kosher salt, freshly ground pepper", "4 dozen small shucked oysters in their liquor (about 1 cup liquor)", "4 large eggs, whisked", "12 cups savory (not sweet) cornbread cut into 3/4\" cubes