Make the cornbread croutons: Preheat oven to 350 degrees.
Cut cornbread into 1-inch and ½-inch cubes. You should have 10 cups. Spread bread over 2 large baking sheets and bake in upper and lower thirds of oven, stirring occasionally and switching position of pans halfway through baking, until completely dry, about 25 minutes. Transfer bread to a large bowl.
Increase oven temperature to 450 degrees and grease a 13x9-inch baking dish.
Heat olive oil in a large skillet over medium heat. Add mushrooms, onion, celery, and garlic, and sauté, stirring occasionally until softened, 10 minutes.
Stir in thyme, sage, smoked paprika, salt and pepper and stir until fragrant, about a minute. Add kale leaves and sauté until wilted, about 5 minutes. If pan is starting to get dry, add a couple Tablespoons of water or stock.
Add vegetables to bread, tossing to combine. Pour stock and eggs over the bread mixture, tossing to coat evenly.
Spread stuffing in the prepared baking dish, dot with butter and cover tightly with foil. Bake in upper third of oven until heated through, about 20 minutes. Remove foil and bake stuffing until top is browned, 10 – 15 minutes more. Stuffing can also be baked in a well-greased 12-cup muffin tin.