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Preheat oven to 250 F. Spread bread cubes in even layer on 2 rimmed baking sheets. Bake until edges have dried, but centers are slightly moist (50-60 minutes). Increase oven temperature to 375 F. Transfer rye cubes to large mixing bowl.
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In large skillet, cook sausage, breaking sausage into small pieces with wooden spoon, until browned (5-7 minutes). Drain; discard any drippings. Transfer sausage to bowl with rye cubes.
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In same skillet, heat butter over medium-high heat until melted. Add leeks, fennel, carrots, mushrooms and wild rice seasoning. Cook, stirring occasionally, until vegetables are softened but not browned (7-9 minutes). Transfer vegetables to bowl with sausage mixture; mix well.
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Stir in 1 cup cheese, parsley, salt and pepper. Whisk together chicken broth and eggs. Pour over stuffing; mix to combine. Spray 3-quart baking dish with no stick cooking spray. Spoon stuffing into baking dish; sprinkle with remaining ½ cup cheese.
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Bake until stuffing is set and crisp on top (35-40 minutes).