In a small sauce pan, heat tangzhong ingredients on medium until a paste forms (about 2 minutes). Allow to cool.
In a stand mixer bowl, add all your ingredients except for butter.
Gradually increase speed to medium-low until dough forms a ball.
On low speed, add softened butter, 1 tablespoon at a time until it’s all incorporated.
Mix on medium-low to medium speed until the dough is smooth and passes the window pane test (about 10-20 minutes)
Transfer to a lightly oiled bowl and allow to rise until doubled.
Once doubled, punch down to deflate.
Divide into 12 equal parts.
Roll out into disks making sure to leave the middle as the thickest part. Place 1 teaspoon pesto and 1 inch cube of low moisture mozzarella in the middle and wrap the dough around it. Gently roll into balls.
Place on a baking sheet lined with parchment paper, lightly cover, and allow to rise again for 30-45 minutes. Brush with egg wash and bake at 350°F for 18-20 minutes. Brush with garlic butter while hot.