Add the butter and milk to a heat-safe bowl and heat until just warm to the touch (about 60–90 seconds in the microwave). The mixture should be warm—not hot.

In the bowl of a stand mixer, combine the all-purpose flour, salt, instant yeast, and granulated sugar.

Pour in the warm milk and butter mixture, then add the egg.

Using a paddle or dough hook attachment, mix on medium speed for 2–3 minutes, until a soft dough forms.

Transfer the dough to a lightly floured surface and knead for 10–15 minutes, until smooth and elastic.

Lightly oil a medium-sized bowl with about 1 tablespoon of vegetable oil. Place the dough inside, brushing a little oil over the top.

Cover with a kitchen towel or plastic wrap and let rise for 1 hour, or until doubled in size.

While the dough rises, mix together the brown sugar, cinnamon, heavy cream, and room-temperature browned butter (or regular butter) until smooth and spreadable.

Once risen, transfer the dough back to a floured surface and roll it out into a thin rectangle.

Spread the filling evenly across the dough, then roll it up tightly into a log.

Cut the dough into rolls using floss or a string for clean edges. Place rolls into a buttered baking pan and cover with a kitchen towel.

Let rise again for about 1 hour, until puffed and nearly doubled.

Bake at 350°F for 28 minutes, or until lightly golden. Let cool for 10 minutes before glazing.

Whisk together powdered sugar, heavy cream, and vanilla until smooth. Pour over warm rolls and enjoy!

Store leftovers in an airtight container for up to 6 days, or in the fridge for up to 10 days.