Preheat the oven to 350˚F. In a 9 x 13-inch oven-safe baking dish, combine rice, 1 cup chicken stock, butter, ½ teaspoon Italian seasoning, and a pinch of salt and pepper. Cover tightly with foil and bake for 30 minutes.
Meanwhile, season the chicken with salt, pepper, paprika, and remaining Italian seasoning. Add oil to a medium skillet over medium-high heat. Once the oil is shimmering, add chicken and cook for about 5 minutes, flipping halfway through, or until golden brown all over, but not yet cooked through. Remove from the pan and cut into small cubes.
To the same skillet, add the onion and cook for 5 minutes. Season with salt and pepper. Add mushrooms and cook for 10 minutes, until they no longer give off moisture. Add garlic and cook for 1 more minute, until fragrant.
Add the remaining 2–3 cups chicken stock and the sour cream, and bring to a gentle simmer. Once it reaches a simmer, stir in the reserved chicken and remove from the heat.
When the rice is done cooking in the oven, uncover and pour the creamy mushroom and chicken mixture on top. Cover again and return to the oven for 15 minutes, until the chicken is cooked through and the casserole sauce is thickened. Serve warm.