Brown the butter

• Melt the butter in a saucepan over medium heat, stirring constantly until it foams and turns golden brown with a nutty aroma and little brown bits.
• Transfer to a heat-safe bowl and let cool slightly, then stir to distribute the browned milk solids.
• Divide into three portions: one for the dough (kept at room temperature), one for the filling and one for the icing (both chilled until soft and spreadable).

Activate the yeast

• Combine the warm milk, granulated sugar and yeast in a bowl.
• Let sit until foamy.

Make the dough

• Add the egg, egg yolk and brown butter to the yeast mixture and mix.
• Stir in the salt and flour, starting with the smaller amount, and mix until a soft dough forms.
• Knead until smooth and elastic, adding more flour only if needed.

First rise

• Place the dough in a lightly greased bowl, cover and let rise until doubled in size.

Make the filling

• Mix the soft brown butter, brown sugar and cinnamon until combined and spreadable.

Shape the rolls

• Roll the dough into a large rectangle on a lightly floured surface.
• Spread the filling evenly all over.
• Slice into 8 strips with a pizza cutter and roll each one up tightly, or roll the whole rectangle and slice.

Second rise

• Place the rolls in a greased 9x13 pan, cover and let rise until puffy.

Bake

• Pour the warm heavy cream over the rolls right before baking.
• Bake at 175 °C until golden.

Make the icing

• Beat the cream cheese and soft brown butter together until smooth.
• Beat in the powdered sugar, vanilla and a pinch of salt until fully combined.

Finish

• Spread the icing over the warm rolls and serve.