To make the cornbread: Preheat the oven to 425°F. Coat a 13x9x2-inch baking dish with the softened butter.
Into a large bowl, sift the cornmeal, flour, sugar, baking powder, baking soda and salt. In a small bowl, whisk the eggs, buttermilk and the 3 tablespoons of melted butter to blend. Make a well in the center of the cornmeal mixture and stir in the buttermilk mixture just until the batter is moistened.
Pour the batter into the prepared baking dish and bake for about 25 minutes, or until the cornbread is golden brown and a toothpick inserted into the center comes out clean. Let cool for about 10 minutes. Remove the cornbread from the baking dish and place on a cooling rack to cool completely. Break the cornbread into 1 1/2-inch pieces and divide among two baking sheets. Leave the cornbread uncovered at room temperature overnight to dry out.
To make the dressing: Preheat the oven to 250°F. Bake the cornbread pieces, stirring often, for about 30 minutes, or until they have dried out but not browned. Let cool. Arrange a rack in the center of the oven and increase the temperature to 350°F.
Meanwhile, heat a large heavy skillet over medium-high heat. Add the oil and sausage and cook, breaking the sausage apart with a wooden spoon, for about 10 minutes, or until it is browned. Using a slotted spoon, transfer the sausage to a very large bowl.
Add the butter to the sausage drippings in the same skillet and stir until melted. Add the onion and celery, and cook, stirring often, for about 10 minutes, or until the vegetables soften slightly. Working in 2 to 3 batches, stir in the greens, letting each batch wilt before adding more. Stir in 1 cup of stock. Reduce the heat to medium. Cover and braise the greens, stirring occasionally and adding an additional 1 cup of stock after the first 15 minutes, for about 30 minutes, or until the greens are tender. Stir in the parsley, sage, rosemary and thyme. Add the greens mixture to the sausage in the bowl. Gently toss the cornbread pieces into the bowl with the sausage and greens mixture.
In a small bowl, whisk together the eggs, salt, pepper and 3 cups of the stock to blend. Gently fold the egg-broth mixture into the cornbread mixture, taking care not to mash the cornbread. Set aside for about 15 minutes, tossing occasionally, to allow the cornbread mixture to absorb most of the liquid. Gently fold in the remaining 1 cup of stock. The mixture will be wet.
Butter a 13x9x2-inch rectangular or oval baking dish. Transfer the dressing to the baking dish, cover with foil and bake for about 50 minutes, or until bubbly around the edges. Uncover the dressing, increase the oven temperature to 375°F, and continue to bake for about 15 minutes, or until it is set and the top is brown and crisp.
Make-Ahead: The cornbread can be dried out, the sausage can be cooked, and the collard greens mixture can be cooked up to 1 day ahead, each covered separately. Keep the cornbread at room temperature and refrigerate the sausage and collard greens mixture.