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Monita is a Recipe Tester for Food52
Yes, corn starch or flour will work as a thickening agent; and the chicken broth can sub for the milk. I make a roux with non-dairy margarine and then add drippings and chicken broth. That works too
Make a roux with the pan drippings including the fat, cook on low to cook the flour, and add stock/wine (or combination of the two) until desired thickness is reached, simmer over low heat, season to taste and serve.
Agree with soupcon -- we always make Turkey gravy dairy-free. In fact, our "recipe" (quotations, because it isn't written down, more like the process my grandmother taught my mother who taught me...) doesn't have any dairy, so was puzzled by the question. If you use cornstarch, just remember to first stir it in a little cool water then place in hot broth/drippings -- if you put it directly in the hot liquid it will clump. The clumps/lumps can be worked out with determined whisking, but best to avoid the problem in the first place.
Any fat can be used to make a roux (hot fat + flour) to which stock (+\-wine etc) is added and briskly stirred to make "gravy" aka a velouté sauce. We usually skim the fat for the pan drippings and/or giblets and use that to make the roux. Using the turkey fat makes for a more intensely turkey gravy.
Plus a cherry on top if you pretty, pretty please.
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