Pre-heat the oven to 425ºF.
Heat a large, ovenproof skillet with the EVOO, two turns of the pan, over medium-high heat. Add the celery, carrots, onion, garlic, chili pepper, salt, pepper and thyme, and sauté to soften the vegetables, 10-12 minutes. Deglaze the pan with the beer or stock.
Stir together the brown sugar, tomato sauce; hot sauce, Worcestershire sauce and vinegar in a bowl. Pour into the skillet and stir to combine. Fold in the chicken. (Let cool and store for a make-ahead meal. Then reheat over medium heat just to warm up while you mix together the cornbread topper.)
To serve immediately, keep the chicken warm over a low flame while you mix the cornbread batter: Follow the package directions for cornbread batter, then stir in the blue cheese and scallions. Pour over the chicken filling in an even layer, transfer the skillet to the oven and bake to golden brown and firm to the touch, about 12-15 minutes.
Cook’s Note: The filling may be transferred to a casserole dish if your skillet cannot transfer to the oven.