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1
Peel and seed squash. Cut into 1-inch chunks; you should have about 3 cups. In a 3- to 4-quart pan over high heat, combine 1/2 cup water with brown sugar and the squash. Bring to a boil, cover, reduce heat to medium, and cook, stirring once, until squash is almost tender when pierced, 8 to 10 minutes. Uncover and cook, occasionally stirring gently, until most of the water is evaporated, 3 to 5 minutes longer. Remove from heat and let cool.
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2
Peel and chop onion. Rinse, stem, seed, and chop bell pepper. Rinse fennel and trim off and discard base of head and tough stalks. Chop enough fennel to make about 1 cup. Rinse mushrooms and slice 1/4 inch thick.
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3
Squeeze sausage from casings and break into chunks into a 12-inch frying pan or 5- to 6-quart pan over medium-high heat; stir often until lightly browned and crumbly, 7 to 10 minutes. Pour sausage into a wire strainer to drain; discard fat.
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4
Preheat oven to 350u00b0. Add butter to unwashed pan over medium-high heat; when melted, add onion, bell pepper, and fennel and stir often until vegetables begin to soften, 7 to 8 minutes. Add mushrooms and stir until limp, about 3 minutes. Remove from heat and stir in sausage, cilantro, sage, and thyme. Add squash.
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5
In a large bowl, whisk together eggs and broth. Break cornbread into 1/2-inch chunks and drop into bowl. Add sausage mixture and stir gently to combine. Scrape dressing into a buttered 9- by 13-inch baking dish and cover with foil.
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6
Bake until hot in the center, 40 to 50 minutes. Uncover and bake until top is crisp and golden brown, 10 to 15 minutes longer.
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7
Cornbread: Preheat oven to 400u00b0. In a bowl, mix 2 boxes (8 1/2 oz. each) corn muffin mix, 3/4 cup milk, and 2 large eggs until blended but still slightly lumpy. Pour batter into a buttered 9- by 13-inch baking pan. Bake until top is golden brown, 15 to 20 minutes. Let cornbread cool in pan on a rack.
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8
Choose lean chorizo in natural casings or, if available, in bulk without casings. You can prepare the dressing through step 4 up to 1 day ahead; cover and chill chorizo mixture, and store cornbread airtight at room temperature. Before continuing with step 5, let chorizo mixture stand at room temperature about 30 minutes.
