Combine the flour and milk (or water) in a non-stick pan or a saucepan. Use a whisk to stir to combine until you don't see any more lumps. Put on the stove and turn the heat to low-medium and keep stirring

The mixture will start to thicken. Remember to keep stirring and don't crank up the heat. If you use an instant-thermometer to measure, it should be about 65 C/149 F (a bit over is not a big deal). The mixture thickens but we don't want to overcook it and the liquid evaporates too much. Which is why using a thermometer helps a lot

The steps are the same as above but the cooking time may be a bit longer, about 4-5 minutes total when you cook over low-medium. I recommend weighing it when you pour it into a container so you know the weight after cooked and you can divide the weight by two when you need to use half of it

Once the tangzhong has reached the desired temperature, remove from the stove and cover with a cling wrap, touching the surface of the tangzhong directly to prevent a "skin" from forming on the surface. Let it sit at room temperature until it cools down completely

Once tangzhong has cooled down completely, you can incorporate it into your recipe

If you have the time, once the tangzhong has cooled down, store it in the fridge for at least 8 hours or up to 2-3 days. This greatly improves the taste of your finished product. When ready to use, you don't need to let it come to a room temperature and it can be used in the recipe right away. I don't find any difference whether I let it comes to room temperature or not before I use it