Caramelize thinly sliced yellow onions in butter and olive oil in a large skillet over low heat until deeply golden, which takes about 25-30 minutes. Add minced garlic and cook for another minute until fragrant.

Deglaze the skillet with dry white wine (if using), then stir in beef broth, fresh thyme leaves, and a bay leaf; simmer for 10 minutes before removing the bay leaf.

Meanwhile, cook orzo pasta in a separate large pot according to package directions until it is al dente, then drain it and set aside.

In the skillet with the onion mixture, melt additional butter, then whisk in all-purpose flour to create a roux and cook for 1 minute. Gradually whisk in the simmering broth until the sauce is thickened.

Stir the cooked shredded chicken and half of the shredded Gruyere cheese into the sauce. Combine this mixture with the cooked orzo, then season with salt and black pepper and mix everything thoroughly.

Transfer the entire chicken and orzo mixture into a 9x13 inch casserole dish. Evenly sprinkle the remaining Gruyere cheese and all of the grated Parmesan cheese over the top.

Bake the casserole at 375°F (190°C) for 20-25 minutes, or until the casserole is bubbly and the cheese topping is golden brown. Allow it to rest for a few minutes before serving.