In a small pan, whisk together water, milk, and flour. Cook over medium heat, stirring constantly, until it thickens into a smooth paste, similar to pudding. Remove from heat and let it cool to room temp.
In a bowl, combine cooled tangzhong, milk, eggs, honey, starter, and cardamom. Warm the milk slightly in the microwave. Add flour and salt. Mix until it just comes together.
Start kneading by hand for 12 min, adding the soft butter gradually until fully incorporated and dough is elastic and smooth. Ideally, knead for 15-20 mins.
Place the dough in a bowl, cover, and let rest for an hour. Perform about 3 stretch and folds and leave at room temperature for 5-6 hours, until doubled in size.
An hour before shaping, take out the salted butter from the fridge to come to room temp. Prepare cardamom sugar by crushing cardamom pods and mixing with sugar.
Roll the dough into a large rectangle, spread the softened butter, sprinkle the cardamom sugar, and fold the dough. Slice into even strips.
Take one strip, gently stretch it, then wrap it around your fingers and tuck it into the middle. Cover with cling film and let proof for 1.5–2 hours until puffy.
Preheat oven to 180°C (350°F). Brush the buns with egg wash and bake for 18–22 mins, until golden.
In a small saucepan, heat sugar, water, and cardamom until sugar dissolves. Brush warm syrup over buns as soon as they come out of the oven.
