Prepare the pan: Line a 9x13 inch metal pan with parchment.
Set up the dip and coating: Stir the melted dipping butter and vanilla together in one small bowl. Mix the brown sugar, cornstarch, and cinnamon together in a second small bowl.
Turn out the dough: Turn the dough out onto a lightly floured counter.
Shape with the Cinnamon Tuck: Pinch off a piece of dough about 84 g. Dip it in the vanilla butter, then roll it generously in the cinnamon sugar. Push your thumbs into the bottom of the piece so the cinnamon sugar is pressed up inside, bring the sides up, and pinch them together underneath into a taut ball. Then do the same with the opposite edges, and close the bottom seam. Redip the top of the roll into the cinnamon sugar. Set it seam side down in the pan, then shape the next piece. Arrange the 12 rolls in three rows of four, close together.
Use the leftover coating: Drizzle any remaining butter between the gaps of the rolls. Sprinkle any cinnamon sugar left in the bowl over the tops and into the gaps between the rolls.
Second proof: Cover the pan and let the rolls rise at room temperature for 1 to 3 hours, until they are puffy, soft, and pressed up against each other.
Preheat: About 20 minutes before the rolls are ready, preheat the oven to 400°F (200°C) with a rack in the center.
Dimple: Gently press your fingertips into the top of each roll.
Bake: Bake for 25 to 30 minutes, until deep golden and the center roll reads 190°F to 200°F on an instant read thermometer. If your oven runs hot, start checking at 20 minutes, and tent loosely with foil if the tops brown too quickly.
Cool: Let the rolls cool in the pan for 20 to 30 minutes.
Make the icing: Stir the powdered sugar, vanilla, salt, and 15 g of milk together, adding the rest of the milk only if needed, until the icing holds a soft peak but still spreads slowly.
Ice: Scoop a round of icing onto the center of each roll and let it settle. Pull apart and serve warm.