1-1/2 to 3 cups low-sodium chicken or turkey broth, divided
1/4 teaspoon salt
Freshly ground pepper to taste
Heat oven to 325°. In a large skillet over medium-high heat, add oil and sausages, stirring and breaking up meat with a wooden spoon, until most is cooked (some still pink), about 8 minutes. Remove sausage to a plate and discard all but 2 tablespoons of oil and rendered fat. Add onion, carrots, and celery; cook, stirring occasionally, until tender, about 10 minutes. Transfer mixture to a large bowl. Add cornbread, parsley, and sage.
Bring broth to a simmer in a small saucepan. Pour 1 cup over stuffing mixture and toss gently (the cornbread will break into smaller pieces). Add as much of the remaining broth as needed, 1/2 cup at a time, until the stuffing feels moist but not wet. Season with salt and pepper. Spoon the stuffing into a prepared casserole and cover with foil. Bake until thoroughly heated, about 25 minutes. Serve warm.