Preheat the oven to 375 F.
Heat 2 tablespoons of EVOO in a large skillet over medium-high heat. Add the chopped chicken chunks and saut them on both sides until golden brown. Remove chicken chunks from skillet and reserve on a plate.
Add another 2 tablespoons of EVOO, the onion, carrot, celery and garlic to the same skillet and cook, stirring occasionally, until the vegetables are tender, 5-6 minutes.
While the veggies are cooking start the sauce: In a medium-size sauce pan, melt the butter over medium-high heat then stir in the flour and cook until light brown, about 1 minute. Whisk the chicken stock and hot sauce into the butter/flour mixture and bring it to a boil. Simmer the gravy until thickened, 2-3 minutes.
Return the reserved chicken chunks to the skillet with the cooked vegetables and add the gravy, stirring to combine. Transfer everything to a 9x11" casserole dish and set aside while you prepare the topping.
In a medium-size mixing bowl, prepare the cornbread according to package directions. Stir the blue cheese crumbles into the cornbread mixture and drop spoonfuls of the batter onto the top of the casserole, covering it completely.
Bake the pot pie until the cornbread is baked through and the filling is hot, 20-30 minutes.