BUTTER: In the microwave, melt 4 tablespoons butter in a medium-sized microwave-safe bowl and set aside to come to room temperature.
YEAST: Meanwhile, in a medium-sized bowl add warmed milk (Note 2). Sprinkle 3 teaspoons yeast and 1/2 tsp sugar right on top. Whisk and let sit 5-10 minutes (It should look creamy/foamy after 5 minutes (see photo). If not, you'll need to begin again or cinnamon rolls won't rise. (Either the yeast is dead or the milk was too hot.)
BUTTER: To the melted butter bowl, add in 2 tsp vanilla, and 2 large eggs. Whisk until smooth and completely combined.
DRY INGREDIENTS: In a very large bowl add 4-1/2 cups flour, remaining 1/2 cup sugar, and 2 tsp salt. Whisk. Make room in the center to add wet ingredients. Use a spatula to scrape every bit of the butter mixture and then the yeast mixture into the middle of the flour bowl. Stir with a strong rubber spatula until a shaggy/thick dough forms with no dry streaks of flour (see photo -- should be sticky/wet). Cover with plastic wrap.
Two options for how to proceed: MAKE CINNAMON ROLLS TODAY: Let dough rise in a draft-free environment (~70 degrees F) for 90-120 minutes or until nearly 3 times the size. (This is 90 mins at my home.) At this point, also melt the 8 tbsp butter (in the microwave) for the filling. Set it aside to cool and harden to softened butter for easy spreading later! (See note 3)MAKE CINNAMON ROLLS TOMORROW: Let dough rise in a draft-free environment (~70 degrees F) for 30 minutes. Then place in the bottom shelf of a fridge and refrigerate for 8 hours up to 12 hours (no longer). Remove and let stand at room temperature for 30 minutes or until dough is about 3 times the initial size. SHAPE CINNAMON ROLLS : Spray a 9x13-inch pan generously with cooking spray. Sprinkle a large clean work surface with flour then tap all your fingers in flour. Tap spatula in the flour. Use flour-dusted spatula to scrape all the dough onto floured surface. Shape dough into an even-sized ball (use flour as needed so it doesn't stick to you). Use a rolling pin to roll it into a wide rectangle, 15x12-inches (15-inch side facing you).
FILL CENTER: Smooth the softened butter evenly over the dough in an even layer. In a small bowl combine 1-1/4 cups brown sugar with 2 tbsp cinnamon and stir. Sprinkle this mixture evenly over dough and then gently press into dough. Tightly roll up the dough into a cylinder. Using a very sharp serrated knife cut cylinder in half. Cut each half in half again to have 4 pieces. Cut each piece into 3 individual rolls for 12 total cinnamon rolls. Place rolls spaced tightly together in prepared pan. Spray a piece of plastic wrap with cooking spray and place gently over rolls. Let rise for 20-30 (up to 45) minutes or until about 75% larger in size.
BAKE: While cinnamon rolls are rising, preheat oven to 350 degrees F. Once rolls have risen, remove plastic wrap. Warm 1/3 cup heavy cream in microwave for 20 seconds then use a pastry brush to gently and evenly brush over all the rolls. Bake for 40-50 minutes or until the surface is a golden brown and rolls sound hollow when tapped (45 mins in my oven). Remove from oven and let slightly cool 5-10 minutes before frosting.
FROSTING: Meanwhile, prepare the frosting. In a large bowl, beat the room-temperature butter and cream cheese until completely smooth. Mix in the vanilla, salt, and cinnamon. Add in the powdered sugar and then beat until the frosting is smooth (it will seem like you need more liquid, but just keep beating; it will come together! Spread over slightly cooled cinnamon rolls and enjoy them warm!