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Combine the corn starch and water in a small bowl and set aside.
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In medium sauce pan whisk together the half-and-half, sugar, rum, and salt. Turn the heat on medium and stir almost continuously, I keep the whisk moving, giving 5 second breaks from time to time.
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When the sauce just begins to boil, give the corn starch/water mixture a quick stir and quickly add it to the sauce. Remember to keep stirring!
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The sauce should thicken within a few seconds.
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Once it reaches the consistency of gravy, remove from heat and add the vanilla and butter, whisk quickly.
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Pour the hot sauce over your favorite bread pudding, ice cream, pound cake, etc.
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Pour over day old donuts, bake at 375° for 20 minutes for a quick brunch. Serve with coffee.
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Pour over unbaked, canned biscuits, bake at 375° for 35 minutes for bread pudding. Serve this bread warm, alone or with vanilla ice cream.