Special equipment: an 8-inch square baking dish
Preheat the oven to 400 degrees F. Butter the bottom and sides of an 8-inch square baking dish.
Heat 2 tablespoons of the butter in a large skillet over medium-high heat. When it begins to sizzle and brown, add the mushrooms, spread out in as close to a single layer as possible. Cook until they have browned on the bottom, about 3 minutes (resist the urge to move them around before this point), then shake the pan, tossing the mushrooms, and season with 1/4 teaspoon salt. Continue cooking until the mushrooms have browned further and are tender, 4 to 5 minutes more. Transfer them with a slotted spoon to a large bowl.
Lower the heat to medium, and add the remaining 1 tablespoon of butter to the skillet. Add the diced celery stalks, and cook, stirring frequently, until soft, 3 to 4 minutes. Add the kale and 1/4 cup water, cover and cook, stirring occasionally, until tender, about 7 minutes. Transfer the mixture to the bowl with the mushrooms.
Add the stuffing mix, celery leaves and sage to the bowl, and toss to combine. Pour 1 1/2 cups water over the mixture, and stir to incorporate. Turn the stuffing out into the prepared baking dish, and bake until browned and crispy on top and hot throughout, 35 to 40 minutes.
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