To make tangzhong: Add 1/2 cup water and 1/3 cup all purpose flour to a small saucepan. Set it on the stove at low heat and whisk until smooth. I used chopsticks but you can use, you know, an actual whisk. Once smooth, let it heat for about 5 minutes or until thickened (see video below), whisking occasionally.
Add tangzhong and 1/2 can coconut cream or full-fat coconut milk to the bowl of a stand mixer.
Keep the saucepan going on low heat. Add 3 tbsp vegan butter or margarine and let it melt, then turn off the stove.
Add the melted butter along with 1/4 cup sugar, 1 tsp salt, and 2½ cups all purpose flour to the bowl, then start mixing in the stand mixer using the dough hook.
When the ingredients are roughly mixed but haven't yet started coming together, add 2½ tsp instant yeast. We want to add it last to avoid the hot butter and tangzhong from killing any yeast.
Now let the stand mixer knead the dough for 12 to 15 minutes. (See Notes.)
The dough should now be soft and smooth. Shape into a ball and let it rest in the bowl, covered, for 1 1/2 hours.
After rising, the dough should be about 1.5x its original size. Take it out of the bowl and flatten into a big circle, pressing out any air pockets.
Slice the circle into eight equal pieces. Roll each piece into a ball (see video) and place into a round baking pan. Or a square one. Whatever you have.
Cover and let rise. After 30 minutes, preheat the oven to 350 °F (175 °C).
Optional: Mix 1 tsp warm water and 2 tsp brown sugar or syrup together in a small cup and gently brush onto the risen rolls.
Put your rolls into the oven at the 40-minutes mark. (My oven takes 10 minutes to preheat from cold. If yours takes longer, start the preheat a bit earlier.)
At 25 minutes, the rolls should be lightly golden. Turn off the heat and let the rolls sit in the oven for 10 minutes before removing to cool. Let rolls cool in pan for another 10 minutes, then transfer to a wire rack.