Process cooked chicken in a food processor to a crumbled consistency.
In a medium skillet, combine chicken and cream cheese, heating over medium-low heat. Melt the cream cheese while stirring, and add ¾ cup cheddar cheese and the hot sauce. (For a thicker filling, reduce the hot sauce by ¼ cup).
Remove mushroom stems by loosening the stems and then popping them out.
Transfer the filling to a piping bag, or use a spoon to fill each mushroom cap with the buffalo chicken filling.
Sprinkle the remaining cheese over the mushrooms.
Bake for 15 minutes. Drizzle with additional hot sauce, if desired.