Combine the active dry yeast with the warm water and wait about 2-3 minutes for it to dissolve. Stir away any remaining yeast clumps before mixing the dough.

Use the dough hook on low speed to mix the flour, sugar, and salt in the stand mixer bowl, then add the yeast water. Stop this initial mixing stage when the loose flour gathers into a rough, shaggy dough.

Knead at medium-high speed for about 8-10 minutes, then form a ball and cover it in a bowl in a warm spot for 45 minutes to 1 hour. The kneaded dough should stretch into a thin, translucent windowpane without tearing, and the first rise should double its volume.

Press the risen dough to release gas, fold it several times, and divide it into 6 equal portions; tuck each portion into a taut ball and arrange on a parchment-lined sheet pan with 2-3 inches between them. Cover the rolls and let them rise in a warm spot for another 45 minutes to 1 hour, until nearly doubled.

Set the oven to 350°F while the shaped rolls finish rising. The buns should look fuller and puffier than they did immediately after shaping.

Brush the nearly doubled rolls with the beaten egg if using, then bake for about 20-25 minutes. Look for a golden exterior and a center temperature of 190°F as the bread’s doneness cue.

Leave the baked rolls to cool at room temperature before cutting. The crust should feel comfortable to hold rather than hot against your fingers.

Whisk the softened cream cheese with the sugar until evenly blended, then spoon the filling into a piping bag or zip-top bag. The mixture should look smooth and pliable, without firm cream cheese lumps.

Whisk the melted butter, milk, sugar, garlic, parsley, and eggs in a large bowl, then keep whisking over a pot of gently simmering water until the sugar dissolves; keep the mixture warm without overheating. The dip should flow freely and look evenly blended, with no cooked egg flecks, while the kosher salt stays reserved for sprinkling.

Raise the oven setting to 400°F for the finishing bake. This hotter bake crisps the coating around the already-baked rolls.

Cut each cooled roll into 8 equal wedges, stopping before the knife reaches the bottom crust. The wedges should open slightly while remaining attached at the base.

Squeeze a line of cream cheese filling into every cut seam. Keep the filling between the wedges so each petal has a creamy edge.

Submerge each filled roll in the garlic butter, letting the dip reach the seams, then turn it upside down to drain before setting it on a parchment-lined sheet pan. The coating should cling to the bread without leaving a large puddle underneath.

Add the remaining filling to the centers, sprinkle with kosher salt, and bake for 8-10 minutes. Remove the rolls when the crust is crisp and golden, with slight bubbling around the edges, before it becomes overly brown.

Wait a few minutes before handling or serving the finished bread. The filling and buttery coating remain hot even after the crust looks ready to pull apart.