Preheat the oven to 350 degrees . Spread the cornbread on a baking sheet and bake until toasted but not dry, about 15 minutes. Let cool, then transfer to a large bowl.
Meanwhile, grease a 9-by-13-inch baking dish. In a large, heavy skillet, cook the bacon over medium-high heat until crisp, about 5 minutes. Drain on paper towels. Crumble the bacon and add to the cornbread. Melt the butter in the drippings in the skillet and add the bell peppers, onion and poblano. Cook, stirring occasionally, until lightly browned, about 10 minutes. Scrape into the bowl with the cornbread and add the chicken broth, eggs, rosemary, 1 tsp. salt and 1/2 tsp. pepper. Mix gently and transfer to the baking dish. Cover with greased foil and bake until hot, about 45 minutes. Uncover and bake until browned and crisp, about 15 minutes.