Warm your milk gently until it feels just barely hot to the touch, somewhere around 100 to 110°F. Pour it into your mixing bowl and stir in the yeast. Let it sit undisturbed for 5 to 10 minutes until it turns foamy and bubbly on top, which tells you it's alive and ready to work.
Whisk the sugar and egg into your yeasty milk until fully combined. Add the flour and salt, then start kneading by hand or with a dough hook. Work the butter in a tablespoon at a time, letting each piece disappear before adding the next, until the dough turns smooth and slightly tacky.
Move your dough into a lightly greased bowl and cover it with a clean towel. Set it somewhere warm and draft-free for 1 to 2 hours. You're looking for it to roughly double in size, which is how you know the yeast has done its job properly.
Once risen, punch the dough down gently to release the air and divide it into six even pieces. Roll each piece into a ball, then flatten it into a round disc about 6 inches wide. Arrange them on a parchment-lined baking sheet with a little breathing room between each one.
Beat your softened cream cheese until it's completely smooth with no lumps. Mix in the vanilla and heavy cream, then gradually add the powdered sugar until the whole thing turns light and fluffy. Scoop it into a piping bag so it's ready to go.
Brush each dough round with egg wash for that glossy finish. Press a shallow well into the center of each one, then pipe a generous swirl of custard right into it. Spoon a little blueberry jam over the custard and scatter fresh blueberries on top.
Stir together melted butter, flour, brown sugar, and cinnamon until it forms buttery little clumps, then sprinkle it generously over each bun. Bake at 375°F for 20 to 25 minutes, until the tops are puffed and deeply golden and the custard looks just set.
Let the buns rest on the pan for about 10 minutes so the custard has time to firm up before you move them. Finish with a light dusting of powdered sugar right before serving for that classic bakery look.