Whisk the 25 g of bread flour and 120 ml of liquid (and any additions from the note below) together in a small saucepan until smooth. Cook over medium-low heat, stirring constantly, until it thickens into a pudding-like paste. Remove from heat and let it cool to room temperature. This is your tangzhong.
In a stand mixer, combine the bread flour, sugar, salt, and yeast. Try to put the salt and yeast on opposite sides of the bowl. Add the warm milk, egg, and the cooled tangzhong paste. Use the dough hook to mix on low until a shaggy dough forms, then knead for about 5 minutes.
Add the softened butter to the dough and continue kneading on medium speed for another 8-10 minutes. The dough should be smooth and elastic.
Form the dough into a tight ball, place it in a greased bowl, cover it, and let it proof in a warm place for about 1 hour, or until it doubles in size. Gently deflate the dough.
Weigh a bowl on the scale (tare it first to account for the weight of the bowl) then weigh the dough. Divide that number by 6. Use a bench scraper to divide your dough into 6 equally weighted pieces. For example: my dough weighed 696 grams, and each piece should weigh 116 grams. Get it as close as possible, being off either way by a gram is fine. NOTE: this specific pan seemed to have the best results at 115 grams per cube so you may have a little leftover dough.
Spray the inside of each square in the pan with baking spray. Roll each weighed piece into an oval, fold the left and right sides in (like a business letter), and roll it up tightly into a scroll. Place the scrolls inside your greased and lidded cube baking pans (seams facing down).
Spray the bottom of the pan lid with baking spray. Close the lid on your pans. Let the dough proof for 45 minutes, or until the dough fills about 80% of the pan.
Preheat your oven to 375°F. Bake with the lid on for about 20 minutes. Remove from the oven, open the lid and turn over to unmold immediately onto a wire rack and let cool. If there was any excess dough that made little "feet" on the bottom of your cubes you can use a knife to slice them off.
Let cool before storing in an airtight container for 2-3 days, or use immediately.