In a large skillet over medium heat, melt 2 tablespoons of the butter; add the onions and season with salt and pepper, to taste. Cook, stirring often, until light golden, about 6 to 8 minutes and remove from the pan to a small plate. Raise the heat to medium-high and add the water, scraping up the brown bits from the bottom of the skillet and allowing the water to simmer just a couple of minutes to infuse in the onion flavor. Remove from the heat.
Put the cornbread in a large mixing bowl. Melt the remaining 6 tablespoons butter in a small pan over medium heat and let it bubble until the milk solids to start to turn golden. Add the sage leaves and briefly fry until beginning to crisp, about 30 seconds. With a slotted spoon, remove sage and put on top of cornbread to drain and crisp. Remove the butter from the heat. Add the eggs and cooked onions to the cornbread and pour the browned butter over the mixture. Season with salt and pepper, to taste. Add the onion infused water, a tablespoon at a time, gently folding, until cornbread is evenly moistened but not soggy. Pour the dressing into a 9 by 11-inch baking dish and bake in the preheated oven until the top is golden brown in color and the dressing is set in the middle, about 30 minutes.