In a large glass jar, combine the toasted walnuts and vodka. Close the lid and let it infuse at room temperature for 24 hours.
After 24 hours, strain the vodka through a fine mesh strainer and discard the walnuts.
In a pot, mix together the water and sugar and bring it to a boil, stirring until the sugar is dissolved. Let it cool.
Pour the infused vodka back into the glass jar and add the cooled sugar syrup.
Cut the vanilla bean lengthwise and scrape out the seeds. Add the seeds and the vanilla bean to the jar.
Add the cinnamon stick, nutmeg, and cloves to the jar.
Close the lid and let the liqueur infuse for another 2 weeks at room temperature, shaking the jar every few days.
After 2 weeks, strain the liqueur through a cheesecloth-lined fine mesh strainer and into a funnel. Pour it into sterilized bottles for storing.
Enjoy your homemade walnut liqueur on its own, over ice, or add it to cocktails for a flavorful twist.