Preheat oven to 350 degrees Fahrenheit. You will need an oven-proof cast iron skillet or Dutch oven with a lid.
Heat the oil in a large Dutch oven with a lid over medium-high heat. Season the chicken pieces with salt and pepper to taste, add to the skillet and fry until golden brown, about 3-4 minutes per side. Remove chicken from the skillet (chicken will not be cooked through).
Add shallots and mushrooms to pan; cook 5 minutes or until mushrooms are slightly browned, stirring occasionally. Add garlic, thyme, and bay leaves. Return chicken to the skillet. Dust everything with flour, mix to combine, and cook for 2 more minutes.
Deglaze with beer over high heat. Cover the skillet with lid, place in the oven and cook for 45 minutes, stirring occasionally. Remove the lid and roast uncovered for 15 more minutes.
Stir in the cream then place the Welsh rarebit pieces on top of the chicken, (it's ok if some pieces have their bottoms in the sauce) and bake for another 10 minutes or until the cheese is golden brown and bubbly.
Sprinkle with parsley. Serve with noodles, mashed potatoes, or rice.
Slice the bread rolls into 1-inch thick slices. Mix all the other ingredients and spread onto the slices, about ½ tablespoon each.
The choice of beer is at your discretion. The darker the beer, the stronger flavor you will have. Amber or dark porter will have a more intense flavor. A lager (which I used and loved), or light beer will give a dish that will appeal to more people.
The Welsh rarebit is optional.
You can cook the chicken on the stovetop. After it's cooked, place in preheated oven to brown the Welsh rarebits, if using.