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In a glass bottle or jar, steep the chopped hazelnuts in the vodka for about 2 weeks in a cool, dark place, gently shaking the bottle every day.
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Gently pour the jar's contents through a regular strainer or sieve, pressing hard on the nuts to release all of their flavor.
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Follow this by two strainings through slightly dampened cheesecloth.
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For true clarity and professional looking results, pour the strained mixture through a large clean coffee filter placed inside a funnel or clean coffee cone; loosely cover with plastic wrap since the process may take several hours.
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In a very small saucepan, combine the sugar and water.
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Bring to a boil over moderately high heat.
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Simmer, uncovered, 5 minutes.
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Let cool to room temperature.
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Stir in the vanilla.
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Funnel the strained hazelnut mixture into a clean, sterilized, glass bottle and then funnel in the sugar syrup.
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Cover tightly; shake to blend.
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Let mature, at room temperature or slightly cooler, for at least three weeks.