Lightly grease a large mixing bowl with oil. Set it aside.
In a microwave-safe bowl, heat the milk in the microwave on high for about 30 to 40 seconds. Use a thermometer to check the temperature of the milk. It should be somewhere around 105ºF to 120ºF. If the milk isn’t hot enough yet, heat it again for 5 to 10 seconds. If the milk is too hot, quickly whisk the milk and let it cool for several minutes.
Add the sugar and yeast to the milk. Stir to hydrate the yeast. Let it sit for 5 to 8 minutes while you prepare the other ingredients. After 5 to 8 minutes, you should see a layer of foam on the top at least 1/4 inch thick (an indication that the yeast is active).
In the bowl of a stand mixer, combine the all-purpose flour and salt. Add the melted butter, condensed milk, egg, tangzhong, and foamy milk/yeast mixture.
Fit the mixer with the dough hook. Mix the dough on low until you don’t see any loose flour on the sides of the bowl. This should take 30 seconds to 1 minute. Then, increase the speed to medium-low and work the dough for 8 minutes. The dough should wrap around the dough hook and the sides of the bowl clean. If you notice dough stuck to the sides of the bowl after a few minutes, turn off the mixer, scrape down the dough, and continue working the dough with the mixer.
Scrape the dough out of the bowl onto a lightly floured surface and knead a few times. The dough likely will feel a little warm, and it should be soft and supple. If the dough is feeling tacky, lightly dust your hands with flour.
Shape the dough into a ball and place inside the greased mixing bowl. Cover the bowl with a damp towel (or a silicone lid) and let it rise in a warm place for about 1 hour, until the dough doubles in size.