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In a medium-size saucepan over medium heat, melt butter and cook until it is a golden amber color.
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Add water and erythritol. Whisk together. Bring to a simmer over medium-high heat while whisking occasionally until all ingredients are fully incorporated.
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Add heavy cream and vanilla.
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Continue to whisk occasionally, the caramel will start to thicken and deepen a bit in color. This will take about 8-12 minutes. Caramel will be thick, but still pourable. Add salt after caramel comes together.
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Do not overcook (this will result in burnt caramel or for the caramel to separate).
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Use immediately or place the caramel in a glass jar or an airtight container. This can be stored in the refrigerator up to about a week. It may be able to last longer than a week, yet since it is a small batch it usually never lasts that long.
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This sauce will harden in the refrigerator, you can place it in the microwave for a couple of seconds or until it melts to the consistency you would like. Be careful not to heat too long as it may separate.
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If it does separate you can put it in a blender and it should come back together.
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Yield: about 1/3 cup