Over medium heat in a large saucepan, combine brown sugar, sugar, and water until mixture starts to boil. Reduce heat and simmer for 5 minutes.

Place vanilla beans and pecans in a gallon-size canning jar (or any gallon-size heat-resistant jar). Pour the hot mixture into the jar and let cool. Once mixture has reached room temperature, add vodka. Cover tightly and store in a dark place at room temperature for 2 weeks. Shake the jar once daily. Strain the mixture through a sieve and discard solids; bottle and store at room temperature. Use in coffee, baking, or cocktails.