Preheat the oven to 350 degrees F. Melt the butter in an 8-inch cast iron skillet over low-medium heat. Add the shallots and celery and sweat until soft and translucent, about 5 minutes.
Add the garlic and continue to sweat another 3-5 minutes.
Add the white wine and let simmer until the liquid is reduced by half.
Meanwhile, combine the walnuts, currants, bread, parsley, and thyme in a medium-sized bowl.
Once the wine is reduced, add the bread mixture to the skillet and toss with a spoon until uniformly moist. Distribute the mixture evenly in the pan and season with salt and pepper.
Place in the pre-heated oven and bake for about 30 minutes, until the top is golden brown and crusty.
Remove from the oven and serve hot.