In the bowl of a stand mixer, combine the eggs, sugar, and salt.
Place the milk in an extra-large measuring cup and microwave for 1 minute or until lukewarm.
Add the milk and yeast to the egg mixture.
Melt the butter in the microwave using the same measuring cup. Add to the bowl of the stand mixture and whisk to combine.
Add half of the flour and whisk again.
Place the dough hook attachment on the mixer, and add the remaining flour to the bowl.
Mix on low speed until everything is combined, and then increase the speed to medium. Mix for 6 minutes.
Place in a large bowl and cover with plastic wrap. Refrigerate for at least 3 hours or overnight.
Sprinkle a work surface with flour and turn the dough out. Let rest for 10 minutes.
Stir together the brown sugar and cinnamon.
Roll the dough out into a 12 x 20-inch rectangle. Spread with the softened butter, and then sprinkle with the cinnamon sugar mixture.
Spray a 13 x 9 baking dish with oil.
Starting at the long side, roll the dough tightly into a log. Slice into 12 pieces and arrange the rolls in the pan.
Cover with plastic wrap and let rise for 1 hour.
Preheat the oven to 350°F. Bake for 45 minutes, covering towards the end if they get too brown. Test the dough by cutting between two rolls with a knife. If the knife comes out doughy, allow them to cook a bit longer.
Allow to cool in the pan for 10 minutes.
Beat together the cream cheese, butter, powdered sugar, vanilla, and salt in the bowl of a stand mixer.
Frost the cinnamon rolls and serve warm.