In the bowl of a stand mixer, whisk together yeast, warm milk, sugar and salt. Add eggs and half the flour. Using the dough hook, mix until it comes together. Add remaining flour and mix until combined. Add butter and knead for 1 minute, until the chunks are incorporated and a ball forms.
Place dough in a well oiled bowl. Cover with a thin towel and let rise in a warm place until doubled, about an hour.
Roll out the dough on a floured surface into a 16x21-inch rectangle. In a bowl, combine brown sugar, cinnamon and salt. Spread the softened butter over the dough. I use my hands, being careful not to rip the dough. Sprinkle the filling over the butter.
Roll the long edge up tightly until you have a long log. Cut in half. Then cut each half in half. You'll have 4 pieces at this point. Cut each piece into equal thirds. Spray a 13x9inch pan with nonstick spray and place the cinnamon rolls evenly in the prepared pan. Cover with a towel and allow to rise for 30 minutes. Preheat oven to 400 degrees. The rolls won't double but will grow enough to be just barely touching.
Remove towel and bake rolls for 12-15 minues, until golden and no longer gooey. Make the frosting while they are cooling. Add butter, cream cheese and sugar to the bowl of a stand mixer. Using the whisk attachment, whisk until light and fluffy, 3 minutes. Add vanilla and salt and mix another minute. Spread over the cinnamon rolls.