Dissolve the yeast in the lukewarm milk with 1 teaspoon of the granulated sugar in a large bowl.
Whisk the yeast, milk, and sugar together and let the mixture sit for 5 minutes to activate the yeast. A good sign yeast is activated is it will start to froth up.
To the bowl of a stand mixer, add the remaining granulated sugar, 1/3 cup of the butter, the salt, the eggs, and 4 cups of the flour, mixing until well-incorporated.
Pour the yeast mixture over the flour mixture.
Using the dough hook attachment, mix until well incorporated and the dough comes clean from the side of the bowl.
Place the dough into a greased bowl.
Cover the bowl and let it rise in a warm place until it has doubled in size, about 1 hour.
In a small bowl, combine the brown sugar and the cinnamon.
Grease a 9x13-inch baking dish with cooking spray.
Using the extra flour, lightly dust a work surface. Roll the dough out on the prepared surface until it is about 16x12-inches wide about 1/4-inch in thickness.
Spread 1/3 cup of the softened butter evenly over one side of the dough.
Sprinkle the cinnamon-sugar evenly over the buttered surface of the dough.
Working carefully, from the long edge, roll the dough evenly down to the bottom edge.
Cut the dough into 1 1/2-inch slices, and place the slices in the prepared baking pan, swirl-side up.
Cover the baking pan with a clean kitchen towel or plastic wrap and let the rolls rise until doubled in size, about 30 minutes.
Preheat the oven to 350 degrees F.
Place the baking pan in the oven and bake until golden-brown, about 20 minutes.
Combine the remaining 6 tablespoons of the butter, the powdered sugar, the cream cheese, the vanilla extract, and the salt in the bowl of a stand mixer.
Mix until the icing is fluffy and smooth.
When the rolls are done cooking, cool them slightly, and then generously spread the icing over top. This helps them melt slightly and drape on the rolls.
Serve warm!