In a small pot combine the milk and flour for the roux. Cook over medium heat whilst whisking until the mix becomes thick.
Combine the milk and yeast together in the bowl of a stand mixer fitted with a dough hook attachment and whisk gently. Add the remaining dough ingredients, including the roux from above, and turn the mixer on low then gradually work it up to medium speed. Knead for about 20 minutes, until the dough is cohesive and shiny. Transfer to an oiled bowl and let rise for about 2 hours (or 12 if using the overnight option) until doubled in size.
Brown the butter (cook on a frying pan as it melts, then sputters and spits then goes almost silent and you can spot lots of brown bits at the bottom) and let cool.
Turn the dough out onto a floured surface and roll into a 13x9” rectangle. Spread a layer of browned butter over the dough, leaving a half inch border. You needn’t use all the butter (it’ll be too much, plus you can use some of it for the glaze) but just enough to give an even layer. Scatter the brown sugar over the butter and sprinkle on the cinnamon.
Roll up the dough from the short side so you have a shorter log. Slice into 9 pieces, using a bread knife or using unwaxed dental floss, and place into an 8 or 9” square pan. Cover with a flour towel and let rise again until puffy and the dough doesn’t fully bounce back when gently pressed.
Preheat the oven to 375 F. If using the heavy cream, pour it into the empty slots between the rolls and tilt the pan sideways to evenly distribute it. Bake for about 35 minutes, until golden - an instant thermometer will read 190 F to show doneness.
Make the glaze by whisking together the powdered sugar, vanilla, salt and milk together. You can add some of the reserved brown butter (especially the dark brown bits) to the glaze. Add more liquid to make it thinner, more powdered sugar for a thicker glaze. Spread over the rolls and serve.
Rolls keep well in an airtight container on the counter overnight and can be reheated in the microwave the next morning.