Preheat the oven to 350°F. Spray a 9×13-inch baking dish with non-stick cooking spray.
Onto a large baking sheet, spread the cornbread cubes in a single layer. Bake for 25 minutes, until lightly toasted. Set aside to cool and increase oven heat to 375° F.
Set a large, deep skillet over medium-high heat and add the butter. When the butter is melted, add poblano peppers, onion, celery, thyme, salt, and black pepper. Cook for 3 minutes, stirring frequently, until veggies are softened.
Remove from heat then add the cornbread, using a large spoon or spatula to combine thoroughly. (If your skillet is not deep enough, transfer mixture to a large bowl for this step.)
In a medium bowl, whisk together the vegan chicken broth and liquid egg substitute. Pour mixture over the cornbread mixture, tossing gently to distribute the liquid throughout.
Transfer to the prepared dish. Cover with aluminum foil and bake for 1 hour.
Remove foil and return to the oven. Continue baking for an additional 15-20 minutes, until golden brown and lightly crisp on top.
All the dressing to set for 10 minutes, then sprinkle with chopped cilantro and serve hot.