In a mixing bowl, combine all the ingredients; stir until well blended. Scoop mixture onto the center of some wax paper and gather the sides to compact the butter. Fold one side over and form a log, tightening it up. Roll it up to the other side and twist the ends tight. To prevent from opening, fold ends under. Chill until it hardens, about 2 hours.
In the bowl of a stand mixer, add yeast, lukewarm milk and honey. Let it sit for 15 minutes or until foamy.
Meanwhile, in a medium bowl, add 2 cups flour (reserve ¾ cup on the side), garlic powder and salt; whisk until well combined and set aside.
Add unsalted butter, egg and ¼ cup Parmesan cheese to yeast. Using a dough hook, mix the ingredients well. Add flour mixture and process on low speed for 3 minutes. Add 1 tablespoons reserved flour at a time to the bowl, mixing well after each addition, until the dough clings around the hook and pulls away from the sides. Increase speed to 4 and knead for 4 minutes.
With oily hands, form dough into a ball by pulling under and transfer to a lightly greased bowl with olive oil. Cover loosely with a clean dish towel and let rise in a warm, draft-free spot (in the oven with temperature off) until doubled in size, about 1 ½ hours.
When rising time is up, punch dough and transfer to a lightly floured work surface. Sprinkle flour on dough and form a ball by pulling under. Using a bench scrapper, cut dough ball in half (sprinkle more flour if needed) and cut each half in half. Form ball with each piece. Cut each ball in half and each of them in half again, pulling under and forming a ball – in total, 32 balls is needed for this recipe.
Preheat oven to 375ºF and place a small ramekin dish upside down in the center of a lightly greased 12”x1” deep dish pizza pan; set aside.
Working with one ball at a time, flatten it out to about 2 ½-inches around and place a piece of mozzarella in the center followed with a small piece of hard garlic butter. Gather the edges together making sure the stuffing mixture is well covered and tightly pinch it closed. Transfer to the prepared pizza pan, leaving a small space in between. Cover and let it proof for 30 minutes.
In a small bowl, combine egg and milk; beat well and set aside.
Brush egg wash on dough balls after rising time is up. Transfer to preheated oven and bake for 30 minutes. Meanwhile, melt garlic butter. Remove from the heat and brush on a generous amount of melted butter and evenly sprinkle on the remaining ¼ cup of Parmesan cheese. Return to oven and bake for 3 minutes or until cheese is somewhat melted.