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1
Trim fat and membranes from giblets, then rinse giblets and pat dry.
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2
Melt butter in a medium saucepan over medium-high heat. Cook celery, carrot, leek, and onion, stirring fairly often, until they begin to brown, 7 to 10 minutes. Reduce heat to medium.
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3
Add giblets, neck, herbs, peppercorns, and the water. Cover and bring to boil, then reduce heat to medium-low. Cook, uncovered, until reduced to about 3 cups, 50 to 60 minutes.
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4
Pour mixture through a fine sieve into a clean medium saucepan and keep warm over medium-low heat.
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5
Roughly chop giblets and shred meat from neck with a fork (discard other solids).
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6
Place reserved roasting pan over two burners. Add wine and bring to a boil, stirring with a wooden spoon to loosen any browned bits on bottom of pan. Remove from heat.
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7
Heat reserved 3 tablespoons pan drippings in a medium saucepan over medium heat. Add the flour, whisking briskly to combine, then continue whisking, cooking until mixture is fragrant and deep golden brown, about 9 minutes.
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8
Whisking vigorously, slowly add hot stock and bring to a boil, then reduce heat to a gentle simmer.
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9
Stir in reserved deglazing liquid, pan drippings, and giblets and neck meat. Season with salt and pepper. Simmer, stirring occasionally, until the gravy has thickened to the consistency of heavy cream, about 20 minutes.
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10
Strain through a fine sieve into a saucepan (discard solids) and keep warm over low heat. Season with more salt and pepper just before serving.
