Make the tangzhong: Combine water, milk and flour in a medium saucepan. Whisk until combined and no lumps remain. Place the saucepan over medium heat and cook the mixture, whisking constantly, until it thickens, about 1-2 minutes. Set aside to cool.
Make the dough: While the tangzhong is cooling, begin preparing the rest of the ingredients for the dough. Combine yeast, cardamom, salt, sugar and flour in a large bowl. Whisk briefly to combine.
Add melted and cooled butter, slightly warm milk, egg and the cooled tangzhong (it can be slightly warm to the touch) to the bowl of a stand mixer. Mix (using the dough hook or dough roller) on medium low until combined. Add dry ingredients and continue mixing until the dough just comes together.
Increase mixer speed to medium and knead mixture for 3-4 minutes or until dough is slightly tacky but not sticky and clears the side of the bowl. It’s okay if it’s sticking to the bottom of the bowl slightly. You can also mix and knead the dough by hand but it will take longer, more like 8-10 minutes.
Cover the bowl with plastic wrap and allow the dough to rise until 1 ½ or 2 times its original size, about 2 hours.
In the meantime, make the filling. Combine butter, flour, salt, brown sugar and cinnamon in a medium bowl. Using a fork, mix ingredients together until a smooth, spreadable paste forms.
Once the dough has risen, preheat the oven to 400 degrees F and move the rack to the center position. Remove the dough from the bowl and place it onto a clean countertop. Roll out with a rolling pin until it is in the shape of a rectangle that is about 15 by 19 inches in size. The dough should be smooth enough that you do not need to add flour during the rolling process. If yours is sticking the rolling pin, however, sprinkle a little flour over the dough as necessary to prevent this from happening.
Using an off-set spatula or your fingers, spread filling in a thin layer over the entire surface of the dough. Roll the dough into a cylinder shape lengthwise and cut into 12 slices, trimming the ends of the cylinder if needed.
Place each sliced bun inside a jumbo muffin tin liner that has been widened slightly on the bottom. Press down on the bun with your fingers to widen slightly. Place 6 buns on a baking sheet. Loosely cover with plastic wrap or a tea towel and set aside. Repeat with remaining 6 buns, placing them on the second baking sheet before covering with plastic wrap. Let covered buns rise for an additional 20 minutes.
Remove the plastic wrap or towel and bake one pan of buns at a time for 13-15 minutes or until golden brown. Repeat with the remaining pan. While the buns are baking, melt the butter and combine the cinnamon and sugar for the topping. Cool slightly and brush with melted butter and sprinkle with cinnamon and sugar mixture. Serve.
Notes
Using jumbo muffin tin liners helps keep the buns contained and keeps them soft and tender. You can simply line your baking sheets with parchment paper and bake the buns directly on the parchment, but they won’t have quite the same tender texture.If your buns rise upward more than you would like, simply pat them down gently with a rubber spatula once they come out of the oven.To substitute active dry yeast for instant: While this recipe calls for instant (or rapid rise) yeast, you can certainly substitute active dry yeast for the instant by proofing it in the warm milk for about 10 minutes prior to adding it to the dough. The amounts stay the same.To make ahead: Either let the dough rise at room temperature until about double in size and then transfer the dough to a 9x13 baking dish and cover it tightly with plastic wrap. Store in the refrigerator until you are ready to shape the buns and proceed with the recipe (up to 24 hours). OR, shape the buns as directed the night before baking and wrap with plastic wrap. Transfer to the refrigerator until you are ready to bake them the following morning. Be sure to give them 45 minutes or so to warm at room temperature before popping them into the oven.To store: These buns are at their very best just after baking, but should you have leftovers, store them on the countertop in an airtight container for up to 2 days. Freeze for longer storage (see below for instructions).To freeze: Once the buns have cooled completely, pop them in a freezer bag or other freezer-safe container and tightly seal. They will keep for about 3 months in the freezer. To reheat, just set the bun or buns on an ovenproof plate and place in 250 degree oven until warmed through.