Oyster-Cornbread Stuffing

Preheat oven to 350 °. Combine broth, sage sprig, and rosemary sprig in a small saucepan; bring to a boil. Remove pan from heat and let stock steep until ready to use. Meanwhile, heat a large skillet over medium heat and cook sausage, breaking it up with a spoon, until cooked through, 7-8 minutes. Using a slotted spoon, transfer sausage to a large bowl, leaving any rendered fat in pan. Melt butter in skillet; add onions and celery and cook until softened, about 10 minutes. Add onion mixture, sliced sage, parsley, and thyme to bowl with sausage. Mix well; season with salt and pepper. Add oysters with liquor, reserved broth (sprigs removed), and eggs; toss to combine. Add cornbread; toss until well blended and cornbread absorbs most of liquid. Spoon stuffing into a 3-quart baking dish. If any liquid remains in bowl, drizzle 1/4 to 1/2 cup over to moisten cornbread (amount varies depending on dryness of cornbread). Bake until browned and liquid is absorbed, 1 hour-1 hour 15 minutes, tenting with foil if top gets too dark.