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Take the turkey out of the brine and discard the brine.
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Don't rinse the turkey. Just pat it extremely dry with paper towels.
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Mix all the rub ingredients and press the mixture generously over every surface of the breast.
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I don't think you need mustard or oil as a binder here. A slightly damp turkey surface should hold that coarse pepper-and-coriander mixture just fine.
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Into the smoker immediately
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Preheat to: 275°F
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I like a fairly restrained smoke for turkey. Apple, cherry, pecan, or a mild hickory would all work. I wouldn't bury this under mesquite.
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Put the breast and any tenderloins into the smoker.
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The original recipe smokes at 250°F and says it can take up to two hours. Moving to 275°F gives us some schedule insurance while still providing plenty of smoking time.
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Start checking the tenderloins after about 45 minutes. They're our secret weapon for the stream because they're likely to finish considerably before the breast.
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Check the breast beginning around 1 hour.
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Cook until the thickest part reaches 165°F. USDA's safe minimum temperature for poultry is 165°F.
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Remove and loosely tent with foil.
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Rest: 15-20 minutes
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For immediate tasting, slice thinly across the grain.
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Chill it before serious slicing
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Once cooled, refrigerate the breast until thoroughly cold — preferably overnight.
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A cold turkey breast will slice much thinner and cleaner than a warm one. If you've got a deli slicer, this is where it earns its keep.
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I would portion it into roughly 4-6 oz packages for refrigerator/freezer use.