Preheat the oven to 350°F (175°C).
Heat 1 tablespoon of the oil in a large Dutch Oven, casserole or Le Creuset casserole over medium heat.
Sauté the onions for about five minutes, stirring almost constantly.
Add the mushrooms and a bit more oil if necessary. Continue to sauté until the mushrooms have softened.
Remove the onions and mushrooms from the pan and keep warm.
Add the remaining oil to the pan, and brown the chicken on all sides until the skin has begun to take on a burnished glow. Finish with the chicken upside down on its breast.
Return the onions and mushrooms to the pan, scattering them over and around the chicken.
Add the carrots, celery, oregano, thyme, a pinch of salt and a good grinding of pepper.
Pour the beer over top of the chicken and vegetables and put the lid on the casserole.
Put the casserole the oven for an hour.
Remove the casserole from the oven and baste the chicken.
Return the casserole to the oven and cook for a further thirty to sixty minutes, depending on the size of the chicken. (The general rule is 20 minutes per pound plus 20 minutes. Chicken is done when it reaches an internal temperature of at least 165°F and no pink remains inside.)
When the chicken is cooked, remove the casserole from the oven and place on a heat proof surface.
To make the gravy, take most of the liquid off the chicken using a baster and transfer it to a medium saucepan.
Bring the liquid in the saucepan up to the boil, stirring constantly.
Mix 1 tablespoon of corn flour with 1 to 2 tablespoons of water to make a smooth paste.
Gradually whisk this paste into the bubbling chicken juices, stirring constantly.
Cook until the mixture thickens up a bit, stirring constantly. Taste for seasoning.
Serve the chicken with the gravy and vegetables.