Preheat oven to 350°F. Grease a 2½-3 quart casserole dish with butter and set aside.
Rinse the rice in a fine mesh strainer. Cook according to package directions, but reduce the cooking time by 10-15 minutes so the rice is slightly undercooked. Drain well and transfer to a large mixing bowl.
While the rice cooks, heat a large skillet over medium-high heat and add 1 tablespoon butter. Add the ground venison in an even layer and season with salt and pepper. Cook for 4-5 minutes, or until browned on the bottom. Flip, season the other side with salt and pepper, break into small pieces, and cook for another 2-3 minutes, until cooked through. Transfer the venison to the bowl with the rice.
Reduce heat to medium. Add the mushrooms to the skillet and season with salt and pepper. Cook for 7-8 minutes, stirring occasionally, until the mushrooms release their liquid and it cooks off. Transfer the mushrooms to the bowl with the venison and rice.
Add the remaining 3 tablespoons butter to the skillet. Once melted, add the celery, carrots, onion, garlic, and thyme. Season with salt and pepper and cook for 3-4 minutes, stirring occasionally, until slightly softened.
Sprinkle the flour over the vegetables and stir to coat. Cook for 1-2 minutes to remove the raw flour taste.
Slowly add the stock, half-and-half, and Worcestershire sauce, stirring to combine. Bring the mixture to a gentle simmer and cook for 6-7 minutes, or until the sauce has slightly thickened. Taste and adjust seasoning with salt and pepper if needed.
Pour the sauce and vegetables into the bowl with the rice mixture and stir to combine. Alternatively, you can add the rice, venison, and mushrooms to the skillet, if your skillet is large enough. Transfer the mixture to the prepared casserole dish and spread evenly.
Lightly grease a piece of foil and cover the casserole (greased side down). Bake for 30-35 minutes, then remove the foil and continue baking for 15-20 minutes, until bubbly and golden brown.
Let the casserole rest for 5 minutes before serving. Top with chopped parsley if desired.
Notes
Cooking the rice slightly underdone ensures it finishes perfectly in the oven.
Ground venison keeps the dish lean and flavorful, but ground beef, elk, or other wild game work just as well.
Undercook the rice slightly so it doesn't become mushy after baking.
Brown the venison well to build flavor before adding it to the casserole.
Let the mushrooms cook down fully. This concentrates their flavor and prevents excess moisture.
If the liquid looks a little thin before baking, that's perfect. It will thicken as it cooks.