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. *If you do not own a mixer, you can do this in a large mixing bowl and in the next step, mix the dough together with a large wooden spoon/silicone spatula. It will take a bit of arm muscle. A hand mixer works, but the sticky dough repeatedly gets stuck in the beaters. Mixing by hand with a wooden spoon or silicone spatula is a better choice.*

Add the remaining sugar (1/2 cup or 100g) 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. Dough will be soft. If it seems too sticky and clings to the sides of the bowl instead of forming a rough mass around the dough hook or spoon, add more flour, 1 Tablespoon at a time, and continue to mix until the dough pulls away from the sides of the bowl but is still moist and tacky. If it feels dry and crumbly, add more milk, 1 teaspoon at a time, mixing well after each addition.

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. (If you’re new to bread-baking, my How to Knead Dough video tutorial can help here.) If the dough becomes too sticky during the kneading process, sprinkle 1 teaspoon of flour at a time on the dough or on the work surface/in the bowl to make a soft, slightly tacky dough. Do not add more flour than you need because you do not want a dry dough. After kneading, the dough should feel smooth, supple, and elastic. Poke it with your finger—if it slowly bounces back, your dough is ready to rise. You can also do a “windowpane test” to see if your dough has been kneaded long enough: tear off a small (roughly golfball-size) piece of dough and gently stretch it out until it’s thin enough for light to pass through it. Hold it up to a window or light. Does light pass through the stretched dough without the dough tearing first? If so, your dough has been kneaded long enough and is ready to rise. If not, keep kneading until it passes the windowpane test.

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 1/2 to 2 hours or until doubled in size. (I always let it rise on the counter and it takes about 2 hours. For a tiny reduction in rise time, see my answer to Where Should Dough Rise? in my Baking with Yeast Guide.)

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. Make sure the dough is smooth and evenly thick. If the dough keeps shrinking as you roll it out, stop what you’re doing, cover it lightly, and let it rest for 10 minutes to relax the gluten. When you return to the dough, it should stretch out much easier.

Spread the softened butter all over the dough. The softer the butter is, the easier it is to spread in this step. (Microwave it for a few seconds to soften if needed.) 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. If some filling spills out, sprinkle it on top of the roll. With an extra-sharp knife, 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. (Or use the overnight option in the Notes below.)

Preheat the oven to 350°F (177°C).

Bake for about 25–28 minutes or until they are lightly browned on top, rotating the pan halfway through. If the tops are browning too quickly, loosely tent a piece of aluminum foil over the top of the pan. Remove pan from the oven and place pan on a cooling rack for about 10 minutes while you make the icing.

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.

Cover leftover frosted or unfrosted rolls tightly and store at room temperature for up to 2 days or in the refrigerator for up to 5 days.