Combine chopped hazelnuts, vodka and brandy in a quart jar and seal. Shake and let steep for 2 weeks, shaking every few days or so.
In a small pot over medium heat, bring water, erythritol and xylitol to a boil. Boil for 5 minutes, until sweeteners dissolve and mixture thickens slightly. Let cool.
Add cooled water/sweetener mixture to the jar, along with hazelnut and vanilla extracts. Seal, shake and let steep for another week.
Place a large sieve over a bowl and line with cheesecloth or coffee filters. Let mixture drain through sieve (you may need to change the coffee filters once or twice to get it all to drain properly).
Notes
Serves 10. Each serving has 2 g of carbs (mostly from the xylitol).