Prepare the Thai tea according to the package instructions and let it cool slightly.
In a shallow bowl, whisk together the eggs, milk, brewed Thai tea, and vanilla extract until well combined.
Heat a pan over medium-low heat and melt the butter.
Dip each Hawaiian roll into the egg mixture, making sure all sides are coated.
Place the coated rolls into the pan and cook until golden brown on all sides, turning as needed for even cooking.
Transfer to a plate and drizzle generously with condensed milk.