Arrange a rack in the middle of the oven and heat to 400°F. Line 2 baking sheets with parchment paper and set aside.

Place the milk, oil, sugar, yeast, and garlic powder in the bowl of a stand mixer and stir to combine. Set the mixture aside for 5 minutes to give the yeast a bubbly jump start. Attach the dough hook to the stand mixer. Add 3 cups of the flour, the egg, and 1 teaspoon of the salt to the yeast mixture and mix on medium speed for 5 minutes. Add the remaining 1 cup flour and mix on medium speed until a sticky dough forms, 10 to 15 minutes.

Generously flour a work surface. Scrape the sticky dough onto the work surface and divide into 12 equal portions (about 2 ¾ ounces each).

Tie each portion into a loose knot: stretch and roll one piece of the dough into 6-inch rope. Fold the ends over each other and tuck one inside the other, making a loose knot. Nestle one piece of mozzarella in the center of the knot. Repeat with the remaining dough and mozzarella.

Arrange 6 knots on each of the prepared baking sheets, about 1 ½ inches apart. Cover loosely with a kitchen towel and let the dough rise for about 10 minutes. The dough should be smooth and less wrinkly, but not quite doubled in size.

Bake until golden-brown, 12 to 15 minutes. Meanwhile, make the garlic butter. Melt the butter in a small saucepan over medium heat. Add the garlic and cook until fragrant but not browned, about 2 minutes. Remove from the heat and stir in the parsley and the remaining ½ teaspoon of salt. Pour the garlic butter into a large bowl.

Remove the rolls from the oven and let cool for 3 minutes. Once the rolls are still warm but cool enough to handle, transfer all them to the bowl of garlic butter. Use a large spoon to gently toss and coat the knots in the garlic butter. Transfer to a serving platter, pour any extra garlic butter over the top of the rolls, and serve warm with lots of napkins.