Start by making the tangzhong. Mix 1 tablespoon of bread flour with 6 tablespoons of whole milk on low heat until it forms a thick paste. Add this to the rest of the bread ingredients (excluding butter) and knead in a standing mixer with a hook attachment for 7-8 minutes at medium-high speed until the dough starts coming together.
Add the softened butter and knead for an additional 5-7 minutes until the dough becomes smooth. If making by hand, the dough may be sticky, so avoid adding too much more flour.
Cover the dough and let it rise for 60-90 minutes, or until it doubles in size.
Once risen, divide the dough into 12 equal portions. Roll each into a ball using your palms. Flatten each ball slightly and add 1-2 spoons of cheese to the center. Pinch together the edges and roll again. Place onto a 9×13” pan lined with parchment paper, seam side down.
Repeat for the other pieces. You can skip the cheese for some rolls if you prefer.
Brush the rolls generously with egg wash and let them rise again for 30 minutes.
Preheat the oven to 350°F. Brush with egg wash once again and bake for 18-20 minutes until golden.
While the rolls are baking, melt butter in a nonstick pan over medium heat. Add garlic, sauté for 1 minute, then turn off the heat and mix in parsley.
Brush the warm rolls with the butter and enjoy! These store well in an airtight container at room temperature for a couple of days; just toast before eating.