In the bowl of an electric stand mixer, combine warm water, yeast, and 0.5 teaspoon of granulated sugar. Whisk well and let rest for 5-10 minutes to proof. If it doesn't puff up, the water was too hot or the yeast is bad.

Add buttermilk, eggs, the remaining 0.5 cup granulated sugar, salt, vanilla extract, and 6 tablespoons of melted butter to the mixer bowl. Fit the mixer with a whisk attachment and blend until combined.

Pour in 2.5 cups of the bread flour and mix until well combined. Switch to a dough hook attachment and add another 1 cup of flour. Knead the mixture until combined.

Continue to knead on moderately low speed for about 5-6 minutes, adding more flour as needed to reach a soft and moist dough. The dough shouldn't stick to the sides of the bowl but can stick to the bottom. You may need around 3.75 cups (approximately 18.75 oz) of flour.

Transfer the dough to an oiled bowl, cover with plastic wrap, and let rise in a warm place until doubled in volume, about 1.5 hours.

Butter a rimmed 15 by 10-inch jelly roll pan and line it with parchment paper. Butter the parchment paper and set aside.

Punch down the dough. Lightly dust a working surface with flour and turn the dough out. Sprinkle the top of the dough with a little flour and roll it out into a 20 by 18-inch rectangle.

Spread the 6 tablespoons of softened butter evenly over the entire surface of the dough. In a small bowl, whisk together the brown sugar and cinnamon. Sprinkle and spread the brown sugar mixture evenly over the butter, leaving about a 0.5-inch border uncovered along all edges.

Starting on an 18-inch side, tightly roll the dough into a cylinder. Pinch the seam to seal.

Cut the roll into 12 equal portions (each should be about 1.5 inches wide). Arrange the rolls, spacing them evenly apart, on the prepared baking sheet.

Cover the rolls loosely with plastic wrap (ensure it fully encloses to keep air out) and let them rise in a warm place until doubled in volume, about 1.5 hours. Near the last 20 minutes of rising, preheat your oven to 375 degrees Fahrenheit.

Bake the rolls in the preheated oven until the centers are no longer doughy, about 18-22 minutes. The center should reach 185 degrees Fahrenheit on an instant-read thermometer. If needed, tent with foil during the last 5 minutes of baking to prevent excess browning.

While the rolls are baking, prepare the icing. In a medium mixing bowl, use an electric hand mixer to whip together the softened butter and cream cheese until smooth and fluffy. Add the vanilla extract and powdered sugar and whip until light and fluffy.

Spread the cream cheese icing over the hot-from-the-oven cinnamon rolls. Serve warm. If you have leftovers, store them in an airtight container once cool and rewarm individually in the microwave for about 15 seconds.