In saucepan, combine brown sugar,sugar and water. Cook over medium-high heat until mixture come to a boil; reduce heat and simmer 5 minutes.
Place pecans and vanilla beans in a 1 gallon jar. Pour hot mixture into a jar and cool. Add vodka and stir well. Cover tightly and store in a dark place at room temp at least 2 weeks. Shake jar gently gently once daily.
Pour mixture through a wire-mesh strainer lined with 2 layers of cheesecloth into a bowl, discarding solids. Pour mixture through a wire-mesh strainer lined with a coffee filter into a bowl. Change filter often. (Mixture will drip slowly) Pour mixture into jars; cover tightly. Store @ room temp.