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.
Gently pour the jar's contents through a regular strainer or sieve, pressing hard on the nuts to release all of their flavor.
Follow this by two strainings through slightly dampened cheesecloth.
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.
In a very small saucepan, combine the sugar and water.
Bring to a boil over moderately high heat.
Simmer, uncovered, 5 minutes.
Let cool to room temperature.
Stir in the vanilla.
Funnel the strained hazelnut mixture into a clean, sterilized, glass bottle and then funnel in the sugar syrup.
Cover tightly; shake to blend.
Let mature, at room temperature or slightly cooler, for at least three weeks.