In a small pot, whisk together the milk and flour over medium heat. Keep stirring until the mixture thickens into a smooth, pudding-like consistency. This step helps create an ultra-soft texture in the final rolls!

In the bowl of a stand mixer fitted with a dough hook, combine the warm milk and yeast, giving it a gentle stir to activate. Add the remaining dough ingredients, including your prepared roux, and start mixing on low speed. Gradually increase to medium and let the dough knead for about 20 minutes until it becomes smooth, elastic, and slightly shiny.

Transfer the dough to a lightly oiled bowl, cover it, and let it rise for about 2 hours (or overnight in the fridge for up to 12 hours) until it has doubled in size.

While the dough is rising, melt your butter in a pan over medium heat. It will bubble and sputter at first, then calm down as brown specks form at the bottom—this is where all the nutty, caramelized flavor comes from! Once browned, remove from heat and let it cool.

Once the dough has risen, turn it out onto a floured surface and roll it into a 13x9-inch rectangle. Spread an even layer of browned butter over the surface, leaving a ½-inch border untouched. (No need to use all the butter—save some for the glaze!)

Sprinkle a generous layer of brown sugar over the butter and finish with a dusting of cinnamon for that classic warm, spiced flavor.

Roll the dough up from the short side into a snug log. Using a bread knife or unwaxed dental floss, slice it into 9 even pieces and place them into an 8- or 9-inch square pan. Cover with a clean kitchen towel and let the rolls rise again until they look puffy and spring back slightly when pressed—this usually takes about 45 minutes to an hour.

Preheat your oven to 375°F (190°C). If using heavy cream for extra richness, pour it into the empty spaces between the rolls and tilt the pan gently to distribute it.

Bake for about 35 minutes, or until the tops are golden brown. For the most accurate doneness check, use an instant thermometer—it should read 190°F when the rolls are fully baked.

While the rolls are baking, whisk together the powdered sugar, vanilla, salt, and milk. For an extra depth of flavor, stir in a little of the reserved browned butter (especially those golden brown bits at the bottom). Adjust the consistency by adding more liquid for a thinner glaze or more powdered sugar for a thicker one.

Once the rolls are out of the oven, let them cool slightly, then drizzle the glaze over the warm rolls. Serve immediately for the ultimate soft, buttery, cinnamon-kissed treat!