Kahlua® Homemade

Combine water and instant coffee in a pot; bring to a boil. Stir light brown sugar and dark brown sugar into coffee, reduce heat, and simmer, stirring every 15 minutes, for 3 hours. Remove from heat and cool completely. Pour coffee mixture into a clean, large glass jar. Add grain alcohol, vanilla extract, and vanilla bean; cover with a tight-fitting lid. Let sit in a dark place, shaking occasionally, for 1 month. Divide into bottles, leaving a piece of vanilla bean in each.