Set the butter, brown sugar and heavy cream in a pot and add the fine sea salt. Once the butter melts and the sugar dissolves the mixture will start to boil. Let it boil vigorously for about 3-4 minutes then take it off the heat and stir in the vanilla.
Pour the caramel into the bottom of a *greased* 13x9 inch cake pan. Tilt the pan so the caramel goes into the edges and is in an even layer. Sprinkle the pecans over the caramel. Set this aside while you shape the rolls.
On a floured surface, roll out the dough to about a 12x18 inch rectangle. Spread the cooled brown butter over the dough, leaving a half inch border on one of the short sides. Mix the brown sugar, cinnamon and salt in a bowl. Spread the brown sugar mixture over the butter in an even layer, using your hands or an offset spatula. If you like, you can add a sprinkle of finely chopped pecans.
Roll up the dough from the longer edge in a tight log. Using unwaxed dental floss or a bread knife, slice the dough into 2 inch rolls. I usually slice off a bit of the edges before I start slicing for the rolls. Lay and arrange the rolls on top of the caramel with space between so they have room to rise and bake. Carefully lay a tea towel over the pan and let rise for 45 minutes.
Preheat the oven to 350 F. Bake the rolls for about 25-30 minutes, until golden and fully puffed. To be sure the rolls are done baking, insert an instant thermometer into the center most roll, the temperature should read 190 F. If the rolls aren’t done but some are over-browning, tent the pan with foil as they finish baking.
Give the rolls about 10 minutes on the counter to cool. Lay a sheet of parchment paper over the rolls and then a large cutting board over the paper. Carefully invert the pan (turn it upside down) and lift the pan away. If there are pecans still stuck to the pan, you can carefully take them out one by one and place them back on the caramel.
These are best served warm and the day of baking but they’ll keep fine at room temperature and a 30 second warm up in the microwave will render them still wonderful the next day.