In a small saucepan, bring the milk to a scalding temperature (when a skin forms on top of the milk, about 170 degrees), stirring frequently. Remove immediately from heat after scalding.
Meanwhile, combine 1/3 cup butter, sugar, and salt in a medium bowl. Pour scalded milk over the top and cool to 110 degrees to 115 degrees, stirring occasionally. Whisk in the eggs.
While the scalded milk mixture is cooling, add the yeast to the warm water (110 degrees) and let it "bloom" for 5 minutes (see note 2).
In an electric mixer fitted with the dough hook attachment, combine 4 1/2 cups flour, yeast, and water. With the motor running on low, slowly drizzle in the scalded milk mixture.
Increase the mixer speed to medium and mix until shiny and smooth, 6 to 10 minutes. If the dough is sticky after 3 minutes, add the remaining ½ cup flour, 1 tablespoon at a time, until the dough comes together. Using a small, microwave-safe dish, melt the remaining butter for 15 to 20 seconds.
Turn out the dough onto a heavily floured surface and shape into a ball. Place in a greased bowl and brush with 1 teaspoon melted butter. Cover the bowl with plastic wrap and let proof (rise) in a warm place (80 degrees to 85 degrees) until doubled in volume, about 1 1/2 to 2 hours (see note 3).
While the dough is rising, mix the filling. In a medium bowl, whisk together brown sugar, cinnamon, and salt until combined.
Coat a 9-inch by 13-inch cake pan with nonstick spray. Turn out the dough onto a lightly floured surface. Roll into a 12-inch by 18-inch rectangle and brush with the remaining melted butter.
Sprinkle filling to within 1/2 inch of the edge of the dough and press into an even layer. Using a bench scraper or metal spatula, loosen the dough from the counter if necessary.
Starting at a long edge of the rectangle, roll the dough to form a tight cylinder. Pinch seam to seal. Arrange cylinder seam side down and cut into 12 equal pieces. Using your hand, slightly flatten each piece of dough to seal open edges and keep the filling in place.
Arrange rolls in prepared cake pan. Cover the rolls with plastic wrap and let proof in a warm place (80 degrees to 85 degrees) until doubled in size, about 30 to 45 minutes (see note 3). Pour heavy cream evenly over the rolls after this second proofing.
While the rolls are proofing the 2nd time, make the icing. In a medium bowl, combine cream cheese, buttermilk, and powdered sugar and stir until smooth.
Preheat the oven to 325 degrees. Bake until the rolls are golden brown, about 25 to 30 minutes. Switch the positions and rotate the orientation of the sheets halfway through baking time. Remove from the oven and immediately drizzle with icing.