Whisk the warm milk, 2 Tablespoons 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 about 5 minutes or until foamy on top. *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.*

On medium speed, beat in the remaining sugar (which should be 1/2 cup/100g) and the softened butter until it is slightly broken up. Add the eggs and salt and beat on medium speed until combined. The butter won’t really be mixing into the mixture, so don’t be alarmed if it stays in pieces. Switch the mixer down to low speed and with it running, add 1 cup of flour at a time, making sure it’s fully incorporated before adding the next. After 4 cups have been added, add the last 1/2 cup and beat until the dough comes together and pulls away from the sides of the bowl, about 3 minutes. Dough will be soft.

Keep the dough in the mixer and beat 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 still feel a little soft. 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 use nonstick spray. Place the dough in the bowl, turning it to coat all sides in the oil. Cover the bowl with aluminum foil, plastic wrap, or a clean kitchen towel. Allow the dough to rise in a relatively warm environment for 2 hours or until double 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 metal or glass 9×13-inch baking dish or line 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. In a small bowl, toss the brown sugar and cinnamon together until combined and then sprinkle evenly over the dough. Top evenly with chopped apples. Tightly roll up the dough to form an 18-inch-long log. Cut into 12 equal rolls. Arrange them in the prepared baking pan. Cover the rolls very tightly with aluminum foil.

Cover the rolls tightly and allow to rise until puffy, about 45-60 minutes.(Or use the overnight option in the Notes below).

Preheat the oven to 375°F (191°C).

Bake for about 25 minutes or until they lightly browned on top. About halfway through baking time, tent a piece of aluminum foil over the pan to prevent the tops from browning too quickly. Remove pan from the oven and place pan on a wire rack for about 10 minutes as you make the icing.

Whisk all of the icing ingredients together and drizzle over warm rolls. Serve warm.

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.