Heat the brown sugar and water together in a small saucepan over medium heat.
Continue to heat, stirring occasionally until the brown sugar has completely dissolved.
Bring the syrup to a boil and boil for 1 to 2 minutes until it thickens slightly. The syrup should have a thick consistency (thicker than water), but not be overly sticky or gooey. It will thicken up significantly as it cools.
Remove the syrup from the stove and let it cool for a few minutes.
Bring a small pot of water to a boil. Add in the tapioca pearls and cook for the time indicated on the package. For quick cooking tapioca pearls, this will be about 5 minutes.
Once cooked through and chewy, strain out the boba pearls and immediately add them to the brown sugar syrup, stirring to make sure they are fully coated in the syrup.
Add the boba pearls and brown sugar syrup to a glass, making sure to drip the syrup down the side of the glass. Add in the ice and milk. Stir well to combine before drinking.
