Add pineapple to a small saucepan. Add just enough water to saucepan to cover pineapple. Set saucepan over high heat to boil. Once boiling, stir and reduce heat to low-medium. Cover and let simmer 20-25 minutes.
Remove saucepan from heat and press pineapple chunks against sides of saucepan with back of a wooden spoon to release juices. Pour pineapple mixture through a strainer into another saucepan and discard pineapple chunks.
Add brown sugar to saucepan with the pineapple juice and stir to dissolve. Set saucepan over high heat and bring to a boil. Once mixture is boiling, reduce heat to medium and let cook for five or so additional minutes. Remove from heat to cool completely, then store in an airtight container in the refrigerator.
To serve, pour 2 tbsp (or more, to taste) of pineapple syrup into iced tea and stir to combine.