Bring the water to a boil in a medium saucepan over high heat. Mix in the erythritol and espresso. Reduce the heat to low and whisk until the erythritol and espresso granules dissolve. Remove the pan from the heat and let stand until cool, about 1 hour.
Mix the vodka and vanilla extract into the cooled espresso mixture.
Transfer the liqueur to a large jar. Seal and store away from light, for 4 to 6 weeks before drinking.
Store in the pantry for up to 6 months. Shake before using.
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Notes
Recipe excerpted from Keto Happy Hour by Kyndra D. Holley, copyright 2018, and reprinted with permission.