Heat a large ovenproof skillet with 2 tablespoons extra-virgin olive oil, 2 turns of the pan, over medium-high heat. Add the celery, carrots, onions, garlic, chile pepper, salt, pepper, and thyme and saute to soften the vegetables, 10 to12 minutes, then deglaze the pan with the beer or stock.
Stir together the brown sugar, tomato sauce, hot sauce, Worcestershire, and vinegar in a bowl and pour into the skillet and stir to combine. Mix in the chicken pieces, using tongs and cool and store for make-ahead meal.
Reheat over medium heat just to warm up while you mix together the cornbread topper or, to serve immediately, keep warm on low while you mix the cornbread batter, then transfer to oven and bake until top is deep golden brown.
Cook's Note: The filling may be transferred to a casserole if your skillet cannot transfer to the oven.
For the topping: Follow package directions for cornbread batter, then stir in the blue cheese and scallions, pour over the chicken filling in an even layer and bake to golden brown and firm to the touch, about 12 to 15 minutes.