Prepare the bread dough - 1st rise

• Add the milk into a small bowl and warm to approximately 100-110°F (38°C), about 30 seconds in the microwave. The milk should be warm, just a bit above body temperature. Add a pinch of sugar and the active dry yeast. Let sit for 5 minutes so the yeast will activate.
• While the yeast activates, add the rest of the ingredients into your mixer bowl.
• Once the yeast is activated, you should see bubbles on the surface of the mixture. Pour it into the mixer bowl. Mix with a spatula until the dough just comes together. Cover with plastic wrap and let rest for 20 minutes.
• Install the dough hook on your mixer (I used a KitchenAid). Start at low speed, then gradually increase to setting 8 out of 10. Knead for 10 to 12 minutes, until the dough is very smooth. Stop the mixer in the middle and scrape the dough from the sides of the bowl. Test the dough by pulling a piece of it using both of your hands. It should stretch into a very thin and translucent sheet. The dough should be wet and a bit sticky.
• Grease a big bowl with a thin layer of oil. Place the dough into the bowl. Cover with plastic wrap and place the bowl in a warm spot. Let rise until the dough doubles in size, about 1 hour.

Prepare the topping

Assemble the bread - 2nd rise

• Line two 13” x 9” (33cm x 23 cm) baking pans with parchment paper. (*Footnote 1)
• Punch the air out of the dough. Transfer it onto a lightly oiled working surface. Divide the dough into 8 even pieces, 81 grams per piece.
• Shape the dough one piece at a time. Tuck the dough onto itself by pinching the dough from all sides into the center using your fingers, creating a round shape. Then roll the dough in a circular motion with your palm against the table, until it forms a round ball. Cover the dough pieces with plastic wrap to prevent them from drying out.
• Work on one dough ball at a time. Use a rolling pin to roll each ball into the shape of a slice of ham, but slightly larger (about 5x7”, or 12x18cm ). Place a piece of ham in the center of the dough. Roll up from the bottom, to form a tight log. Roll the log a few times to smooth it out. Pinch both ends to seal.
• Fold the dough log lengthwise in half, pinching the ends to seal once more (it looks like a water drop shape). Turn the dough onto its side, from 1/2” (1cm) of the pinched side, slice cleanly through the center lengthwise with a bench scraper or sharp knife, leaving the pinched side unsliced. Carefully pull the two cut pieces apart, laying them out flat on the lined baking sheet. Press the center slightly to avoid large gaps in between. Repeat to finish assembling all the buns.
• Cover the baking pan with plastic wrap. Let rest again for another 35 to 45 minutes, until the size has doubled.

Final assembly and baking

• Preheat the oven to 350°F (176°C).
• Whisk the egg in a small bowl to make an egg wash.
• Mix the mayo, shredded cheese, and dried parsley together in a small bowl for the filling.
• Once the bread is done proofing, gently brush the top with egg wash.
• Add about 2 tablespoons of the cheese-mayo mixture onto the center of each bun.
• Bake at 350°F (176°C) for 18 minutes, or until the top turns golden. Let the bread cool slightly, then they are ready to serve.

Store and reheat

• Once the bread has cooled completely, store the bread in an airtight container at room temperature if planning to serve within the day. Store in the refrigerator for up to 2 days, or in the freezer for up to 3 months. Reheat in the oven at 350°F (176°C) until warmed through before serving, for the best texture.