Warm 1 cup of milk (100-110 degrees F.), careful not to make it too hot. Dissolve the 2 ¼ teaspoons of active dry yeast, 1 teaspoon from the ½ cup of granulated sugar, and allow it to sit for 5 to 10 minutes. The yeast will proof and become fragrant and foamy. If not try it again, the yeast may be bad or the milk too hot.
Using a stand mixer with a dough hook attachment, add the rest of the ½ cup of granulated sugar, ⅓ cup melted butter, 1 teaspoon salt, 2 large eggs, 4 ½ cups all-purpose flour, and mix until well combined.
Add the yeast mixture to the sugar mixture and mix well on medium-low speed until combined (about 6 to 8 minutes) and the dough has formed. The dough will be soft but will stick onto itself. If you find it is too wet and not coming together to form a soft dough ball, add an additional 1 tablespoon or two of additional all-purpose flour and mix a little longer.
Lightly oil a large bowl or spray with non-stick cooking spray, add the dough ball, and allow to rise in a warm place for 1 to 1 ½ hours or until the dough has doubled in size
In a small bowl, stir together the 1 cup brown sugar and 3 tablespoons ground cinnamon until combined.
Prepare a 9x13-inch rectangle baking dish by spraying with non-stick cooking spray.
Lightly flour a clean surface and roll out the dough into an even rectangle (17" x 14") about ¼ inch thick.
Evenly spread ⅓ cup softened butter over the dough and sprinkle with the cinnamon-sugar mixture.
Working from the long edge of the rectangle, carefully roll the dough from the top edge to the bottom edge.
Using a knife or unflavored dental floss, cut the dough into even 1 ½ inch thick slices and place into the prepared baking dish.
Cover the baking dish with a clean kitchen towel and allow it to rise for 30 minutes or until it doubles in size.
Preheat the oven to 350 degrees F. and place the baking pan in the oven to bake for 20 minutes or until bubbly and light golden brown. Carefully remove them from the oven and allow them to cool in the baking dish.
While the rolls cool, make the cream cheese frosting using a mixer by combining the 6 tablespoons butter, 1 ½ cups powdered sugar, ¼ cup cream cheese, and ½ teaspoon vanilla extract until smooth and mixed well.
Spread the frosting generously over the top of the warm cinnamon rolls.
Serve warm and store in an airtight container in the refrigerator up to 4 days.