Preheat the oven to 375 degrees F. Butter a 9 by 13-inch casserole dish.
In a large saucepan, combine the water, thyme, bay leaf, and salt and bring to a boil over medium heat. Add the chicken and simmer until cooked through, about 15 minutes, depending on thickness of the chicken. Remove the chicken to a cutting board. When cool enough to handle, dice into 1/2-inch cubes and reserve.
Return the water to a boil, add the wild rice, and cover. Cook over medium heat until the rice grains split, 40 to 45 minutes. Drain the excess water, transfer the rice to a bowl and set aside.
In a small pot, over medium heat, add 2 tablespoons of butter. When the butter is melted add the brown sugar, cranberries, rosemary, bread crumbs, and a pinch of salt. Stir until the sugar is dissolved and the mixture is uniform. Transfer to a bowl and set aside. In a large straight-sided saute pan over medium-high heat, melt 2 tablespoons butter. Add the mushrooms, onions, and a pinch of salt. Saute until the mushrooms are browned, about 5 minutes. Add the heavy cream and the cinnamon, bring to a boil, then reduce the heat and simmer about 2 minutes to thicken slightly. Add the Gruyere and mix to incorporate. Add the rice and chicken to the pot and stir to combine. Season the mixture with salt and pepper, to taste, then transfer it to the prepared casserole dish. Spread the cranberry mixture evenly over the top of the casserole and bake until golden and bubbling, about 15 to 20 minutes. Remove from the oven and serve hot.