Heat oven to 400°F. Grease a 13x9-inch baking dish with butter.
Stir corn muffin mix, 2/3 cup broth, and 2 eggs in a large bowl until combined, the batter will be a little lumpy. Pour into prepared baking dish. Bake until golden brown, 20 to 25 minutes. Let cool 30 minutes before coarsely crumbling into a large bowl. Meanwhile, reduce oven temperature to 375°F. Grease a 13x9-inch baking dish with butter and set aside.
Melt butter in a large skillet over medium heat; add onion and bell pepper and cook 5 minutes or until tender. Add cumin, oregano and hot sauce, if desired and cook 1 minute or until fragrant. Remove from heat, add remaining 2 cups broth, and stir to combine, scraping up any brown bits from the bottom of the pan.
Pour onion mixture over crumbled cornbread. Add corn, chiles, and remaining 2 eggs and gently stir until cornbread is evenly moistened. Spoon evenly into the baking dish, then gently fluff the surface with a fork. Bake until the edges are deep golden brown, 35 to 40 minutes. Garnish with green onions if desired.
*Note: Seven cups coarsely crumbled cornbread of your own recipe can be used instead of cornbread prepared from mix, 2/3 cup broth and 2 eggs.