Add the half and half and brown sugar to a small saucepan. Warm over low heat, stirring frequently, until the brown sugar is completely dissolved, about 2–3 minutes. Do not allow the mixture to simmer.
Remove the saucepan from the heat and stir in the vanilla extract until well combined.
Allow the brown sugar creamer to cool, then transfer it to a covered container and store it in the refrigerator.
Notes
Stir or shake the creamer before each use if any separation occurs during refrigeration.
Let the creamer rest in the refrigerator for a few hours for the brown sugar and vanilla flavors to become more rounded.
Use the freshness date of the half and half as a guide for storage, particularly if the carton was already open when you made the creamer.