Cold brew coffee by combining grounds and 1 ¼ cups water into a sealable glass jar, shaking it, then refrigerating mixture for 12 hours (see notes). Strain through a coffee filter into another sealable glass jar.
Combine sugar and 1 cup water in a pot and bring to a boil. Remove from heat and let syrup cool to room temperature.
Add cooled syrup, vanilla bean, and rum to glass jar that contains coffee. Let mixture steep 3 days, then remove vanilla bean and bottle liqueur.
