Whisk the warm milk, 2 Tablespoons of sugar, and the yeast together in the bowl of your stand mixer fitted with a dough hook or paddle attachment. Cover and allow mixture to sit for 5–10 minutes or until foamy on the surface.

Add the remaining sugar and the butter and beat on medium speed until the butter is slightly broken up. Add about 1 cup (125g) of the flour, the eggs, and salt and beat on low speed for 30 seconds. Scrape down the sides of the bowl, then add the remaining flour. Beat on medium speed until the dough comes together and pulls away from the sides of the bowl, about 2 minutes.

Keep the dough in the mixer (and switch to the dough hook if you used the paddle) and beat on low speed for an additional 5 full minutes, or knead by hand on a lightly floured surface for 5 full minutes.

Lightly grease a large bowl with oil or butter (or use nonstick spray). Place the dough in the bowl, turning it to coat all sides in the oil. Cover the bowl with plastic wrap or a clean kitchen towel. Allow the dough to rise at room temperature for 1 and ½ to 2 hours or until doubled in size.

Grease the bottom and sides of a 9×13-inch baking dish (glass or metal) or line it with parchment paper.

Punch down the dough to release the air. Place dough on a lightly floured work surface and using a lightly floured rolling pin, roll dough into a 12×18-inch rectangle.

Spread the softened butter all over the dough. In a small bowl, mix the brown sugar and cinnamon together. Sprinkle evenly over the butter. Tightly roll up the dough to form an 18-inch-long log. Cut into 12 even rolls, about 1.5 inches thick. Arrange in the prepared baking pan.

Cover the pan and allow the rolls to rise until puffy, about 1 hour.

Preheat the oven to 350°F (177°C). Bake for about 25–28 minutes or until they are lightly browned on top.

In a large bowl using a handheld or stand mixer fitted with a paddle or whisk attachment, beat the cream cheese on medium speed until smooth and creamy. Add the confectioners’ sugar, cream/milk, and vanilla. Beat on low speed for 30 seconds, then increase to high speed and beat for 1 minute. Spread the icing over the warm rolls and serve immediately.