Add the ½ cup light brown sugar and ¼ cup water into a small pot and heat on medium low, mixing gently until all the sugar is dissolved. You can continue to let it thicken to your preference.
In a bowl, combine 3 tbsp sugar, 1 egg yolk, and 2 tsp corn starch. Gradually add in ¼ cup hot cream, mixing to temper the eggs so they don't scramble, then add in 1 tsp vanilla. Add the mixture to the other ¼ cup hot cream in the pot and mix continuously until the custard thickens.
Once the custard cools, add in about ½ cup whipped cream and fold to combine.
Add the cooked boba to the brown sugar syrup and custard mixture.
