Mix flour, yeast, sugar, and salt. Add milk and egg and mix to a soft dough, then knead until smooth and elastic. Knead in the butter and keep going until fully incorporated. Cover and leave to rise until doubled (about 60–90 minutes).Quick proof tip: for a faster rise, place the covered bowl in a sink with a little warm water (bath-warm, not hot).
Mix the filling ingredients into a spreadable paste.
Roll the dough into a rectangle. Spread filling over the surface. Roll up tightly, slice into 12 pieces, and place in a parchment-lined snug tray.
Let the buns rise until puffy and touching (around 60 minutes), then bake at 180°C (160°C fan) for 22–27 minutes until golden.
Beat cream cheese and butter smooth, mix in icing sugar, then add espresso, vanilla, salt, and a little lemon juice to taste. Spread over warm buns.