In a bowl, whisk together flour, salt, instant yeast, and sugar.
Add warm milk (95-105 degrees F), ½ beaten egg, and softened butter. Mix until shaggy dough forms.
Knead 6–8 minutes until smooth and elastic. Check with the windowpane test: stretch a small piece — it should form a thin, translucent 'window' without tearing.
Place in a greased bowl, cover, and let rise until doubled, about 45–60 minutes.
Stir together softened butter, brown sugar, cinnamon, and pinch of salt.
Roll dough into a 6 × 12-inch rectangle and spread filling evenly.
Slice into two long strips. Roll one strip tightly, then wrap the second around it to form one large spiral.
Place in a greased 6-inch cake pan (or small skillet/ramekin). Cover loosely and let rise 20–30 minutes, until puffy.
In a small saucepan, melt butter and cook until golden brown and nutty. Let cool slightly. Beat cream cheese until smooth, then add browned butter, powdered sugar, vanilla, and milk/cream. Mix until creamy.
Preheat oven to 350°F (175°C). Just before baking, pour 2–3 tbsp heavy cream over the rolls (optional, for a gooier texture). Bake 22–28 minutes, until golden brown and center registers 190–195°F. Tent with foil if browning too quickly.
Cool 10 minutes before frosting.
