Pour the water and flour into a small saucepan.  Set over low heat, whisking constantly, until no lumps remain, the tangzhong has thickened, and the whisk leaves trails in the mixture.

Pour the tangzhong into a small bowl and immediately cover with plastic wrap to prevent its surface from drying out.  Set aside to cool to room temperature, then use immediately or refrigerate for later use.

Pour the flour into a medium mixing bowl and add the salt and yeast on opposite sides of the bowl, stirring each one into the flour with your finger.  Be sure the salt doesn't touch the yeast directly, as it can kill the yeast or stunt its growth.

Add the sugar, cooled tangzhong, and one egg to the mixture, then pour in half of the cream and butter mixture.  Mix with your hand to form a somewhat sticky dough, gradually adding more of the cream and butter mixture as needed.  Make sure to pick up all the flour from the sides of the bowl.

Lightly butter an 8-inch round cake pan and a piece of plastic wrap to cover the bread later.

Turn out the risen dough onto a lightly floured surface and punch it down all over to knock out the large pockets of gas inside.

Divide the dough into seven equal pieces, using a kitchen scale for accuracy.

Roll each piece into a tight ball and space them equally apart inside the prepared pan.  Cover with the buttered plastic wrap and set aside to rise until their sides are touching and the dough is springy, about 45 minutes.