In a large bowl or stand mixer, combine bread flour, salt, eggs, sugar, yeast, warm milk, and melted butter until mixed
Knead by hand or with a dough hook until the dough is smooth, stretchy, and passes the windowpane test
Shape the dough into a smooth ball, place in a lightly oiled bowl, cover, and let rise for 1 hour until doubled
Punch down the dough, knead briefly, divide into 6 equal pieces, and shape each piece into a smooth ball
Place the dough balls on a parchment-lined baking sheet, cover loosely, and let rise for 30 minutes
Mix 1 egg with 2 tbsp water for the egg wash, brush over the buns if desired, and bake at 350°F for 18–20 minutes until golden brown
Beat cream cheese, sugar, and heavy cream together until smooth and fluffy
In another bowl, mix melted butter, egg, milk, garlic, honey, and parsley to make the garlic butter coating
Once the buns are cool enough to handle, cut each bun ¾ of the way down into 6 equal sections without cutting all the way through
Pipe the cream cheese filling evenly into each slit
Dip each filled bun into the garlic butter mixture, coating the top, sides, and bottom well
Return the coated buns to the baking sheet and bake again at 350°F for 8–10 minutes until the coating is set
Let cool slightly and serve warm