Preheat oven to 400°F. Arrange cornbread in an even layer on a baking sheet and toast for about 10 minutes, or until lightly golden brown. Remove from oven and let cool.
Reduce oven temperature to 350°F. Grease an 8×11-inch dish and set aside.
Melt 1 tablespoon butter in a large skillet over medium heat. Add the sausage, breaking it up with a wooden spoon until it starts to brown, about five minutes. Use a slotted spoon to transfer to a large bowl.
Melt another tablespoon of butter in the pan and add onion and celery. Season with salt and pepper and cook until soft, 8-10 minutes. Stir in garlic and cook until fragrant, about 30 seconds. Transfer vegetables to bowl with sausage.
Add white wine to pan and cook until reduced by half. Stir in kale and increase heat to high. Toss the greens in the liquid, then cover and cook for about 5 minutes, until soft. Remove lid and continue to cook until all the liquid has evaporated, another 1 to 2 minutes.
Transfer kale to bowl with sausage, along with stock, eggs and herbs. Gently fold in toasted cornbread, stirring just until everything is moist. Spread into prepared baking dish, cover with foil and bake for 20 minutes. Meanwhile, melt remaining 2 tablespoons butter in a small bowl. Uncover the stuffing and brush the surface with melted butter. Bake another 30-40 minutes, or until golden brown and crisp.