Preheat oven to 400°F. Spray a 9×13-inch baking dish with nonstick baking spray.
Grate the butter using the fine edge of a grater. Grate onto parchment paper, then place in the freezer while you prepare the remaining ingredients.
In a large bowl, whisk together the flour, granulated sugar, baking soda, and baking powder.
Remove the grated butter from the freezer. Using a fork or pastry cutter, incorporate the butter into the dry ingredients until the mixture resembles coarse crumbs.
Pour in the buttermilk and stir gently until just combined. Do not overmix; the dough should be slightly shaggy but hold together.
Turn the dough out onto a lightly floured surface. Use your hands to gather any dry bits and gently press them into the dough. If needed, sprinkle a little flour underneath to prevent sticking.
Roll the dough into a 10×15-inch rectangle, about ¼ inch thick.
In a small bowl, combine the brown sugar, cinnamon, and salt.
Brush the melted butter evenly over the surface of the dough. Sprinkle the brown sugar mixture evenly over the buttered dough.
Starting from the long edge, roll the dough up tightly into a log. Using a very sharp knife, cut the log into 12 equal rolls.
Place the rolls into the prepared 9×13-inch baking dish, spacing them evenly.
Bake for 18-22 minutes, or until the rolls are golden brown and cooked through.
When the rolls are almost done baking, prepare the frosting. In a stand mixer fitted with the paddle attachment, combine the cream cheese, butter, confectioners' sugar, vanilla extract, and salt. Mix on low until just combined. Then, increase speed to high and beat for 4–5 minutes until light and fluffy.
Spread the frosting over the warm rolls directly in the pan. Or, invert the rolls onto a serving plate and then frost.
Serve warm.