Coat a large wide pot with olive oil and toss in the celery and onions. Season with salt and cook the veggies over medium-high heat until soft and very aromatic, 8 to 10 minutes. Add the garlic and cook for an additional 1 to 2 minutes. Add the mushrooms and cook for 3 to 4 minutes.
Add the sausage and cook, breaking it into really small pieces with a metal spoon or spatula, until it's really brown and yummy, 12 to 15 minutes.
Add the white wine and cook until it has evaporated by half. (The mix will be pretty soupy, and that's okay.)
Combine the bread with the sausage mixture in a large bowl. Toss in the walnuts and sage and pour about half the chicken stock into the bowl. Using your hands, work to combine everything well -- really get in there and squish it up; it's fun! Add the remaining stock as needed to create a really moist mix. Taste and season with salt, if needed.
Transfer the mixture to a 9-by-13-inch baking dish and cover with foil. Bake until the stuffing is hot all the way through, about 30 minutes, then remove the foil and bake to brown the top, another 15 minutes.