Preheat the oven to 400°F; position one rack in the center.
In a large skillet or 3 quart cassoulet, heat the olive oil over medium-high heat until shimmering. Brown the thighs on one side only, and remove to a plate (you'll probably need to do this in batches).
Add the butter and garlic, and saute the garlic until fragrant (just 30 seconds or so). Add the orzo and rice and stir to coat with the butter. Add the stock, beer, thyme, and rosemary, and stir to level out the rice and liquids. Nestle the chicken thighs, onion wedges, mushrooms, and squash ribbons in the rice mixture, and top with a big pinch of salt. Let the liquids come to a gentle boil (should just take a few minutes).
Cover the skillet (use foil, if you don't have a lid), and place in the oven. Cook for 45 to 50 minutes. Most (but not all) of the liquid should be absorbed. If the liquid in the pan seems excessive, remove the cover and bake for 5 minutes more.
Remove from the oven and let rest, uncovered, for 5 minutes. Sprinkle with the parsley and a few grinds of black pepper before serving.