Heat oil in a large skillet over medium heat. Add sausage, and cook, breaking it into small pieces with a wooden spoon, until browned, 4 to 5 minutes. Using a slotted spoon, transfer sausage to a medium bowl.
Add onion and celery to drippings in skillet, adding more oil if necessary. Cook, stirring occasionally, until onions are translucent and celery is tender, about 6 minutes. Add mushrooms and thyme, and cook, stirring occasionally, until mushrooms are softened, about 2 minutes. Add wine and raisins, and stir, scraping browned bits from bottom of pan. Simmer until reduced by half, 2 to 3 minutes. Stir in cooked sausage, remove from heat, and let cool slightly in pan.
Working in batches, pulse sausage mixture in a food processor until very finely chopped. (If baking the stuffing outside a turkey, pulse only until coarsely chopped.) Transfer to a medium bowl. Stir in breadcrumbs and pecans, and season with salt and pepper. Add egg, and stir to combine. Let cool to room temperature.
To cook stuffing in a turkey: Stuff as directed (see Rolled Turkey recipe). To bake all of the stuffing outside a turkey: Spoon into a buttered 9-by-13-inch baking dish. Cover with parchment, then foil, and bake in a 375-degree oven for 25 minutes. Uncover, and continue to bake until golden brown, 15 to 20 minutes.
Make-ahead tip: Prepare stuffing and spread over turkey the day before. If baking stuffing outside the bird, assemble the day before, cover, refrigerate, and bake just before serving.