In a large frying pan over medium heat, cook the sausages, breaking up the clumps with a wooden spoon and stirring occasionally, until lightly browned, about 10 minutes. Transfer to a large bowl and discard the fat in the pan.
Return the pan to low heat and add the oil. Add the onions and celery and cook, stirring occasionally, until soft, 7–8 minutes. Add to the bowl with the sausage. Add the bread cubes, apricots, and parsley and toss to mix. Season with the sage, thyme, nutmeg, and salt and pepper to taste and toss again. Moisten with the broth,
Allow the stuffing to cool to room temperature. Then, following the directions, stuff two-thirds of the stuffing into the bird. Put the rest of the stuffing into a small, buttered baking dish and cover tightly with aluminum foil. During the last hour the turkey is roasting, bake the extra stuffing in the oven alongside the turkey for 30 minutes. Uncover and continue to bake until heated through and lightly browned and crisp on top, 20–30 minutes longer. (Alternatively, if you do not want to stuff the turkey, transfer the stuffing—now called dressing—to a buttered 4-quart baking dish and bake according to the above instructions.)
Using a large spoon, transfer the stuffing from the turkey cavity to a warmed serving dish. Keep warm until ready to serve.