Preheat oven to 400 degrees F.
Heat a large 3-5 quart brasier or dutch oven over high heat. Add the 2 tablespoons olive oil. Place the chicken in a ziplock bag and toss with the remaining 2 tablespoons olive oil, thyme, rosemary, brown sugar, and a good pinch of both salt and pepper. Add the chicken to the hot brasier (or whatever you are using) and sear on both sides until lightly browned, about 2 minutes per side. Remove the chicken from the pan. Repeat with any remaining chicken, remove from the pan.
Reduce the heat to medium and add 2 tablespoons butter. Add the orzo and cook about 1-2 minutes or until lightly toasted and golden, stirring often (watch this closely as it burns fast). Add the wild rice and toast another 1-2 minutes, stirring often. Toss in the carrots and mushrooms, cook 2 minutes. Add the chicken broth, beer and another pinch of salt and pepper. Use a wooden spoon to scrape up any browned bits off the bottom of the pan. Stir in the parsley and sage. Remove from the heat.
Place the chicken right on top of the rice. Drizzle with lemon juice, season lightly with salt and pepper. Add the onion quarters and garlic (you can leave the skin on the garlic). Throw in a few sprigs of fresh thyme and rosemary. Divide the remaining 4 tablespoons of butter over the chicken pieces. Cover the pan tightly with a lid (or tin foil if you have to, but a tight fitting lid works best).
Bake for 45 minutes to 1 hour or until the liquid is absorbed and the rice is cooked. During the last 5 minutes of cooking remove the lid and allow the chicken to brown a little more, if needed, add in 1/2 cup more chicken broth to keep the rice from getting dry.
To serve, plate the rice and chicken, if desired, drizzle with cider (recipe below).
If desired, make the cider drizzle while the chicken roasts. Add the cider to a sauce pot and bring to a boil. Boil for 15-20 minutes or until the cider is reduced and thick + syrupy. Remove from the heat and stir in the butter.