1) First, make the dough. If you're using active dry yeast, dissolve it with a pinch of sugar in 2 tablespoons in the lukewarm water. Let the yeast and water sit at room temperature for 15 minutes, until the mixture has bubbled and expanded. If you're using instant yeast, you can skip this step.
2) Combine the dissolved yeast (or instant yeast) with the remainder of the dough ingredients. Mix and knead everything togetherby hand, mixer or bread machine set on the dough cycletill you've made a smooth dough. If you're kneading in a stand mixer, it should take about 7 minutes at second speed, and the dough should barely clean the sides of the bowl, perhaps sticking a bit at the bottom. In a bread machine (or by hand), it should form a smooth ball.
3) Place the dough in a lightly greased bowl. Cover the bowl, and allow the dough to rise, at room temperature, till it's nearly doubled in bulk, about 1 to 2 hours. Rising may take longer, especially if you've kneaded by hand. Give it enough time to become quite puffy.
4) While the dough is rising, lightly grease two 9" round cake pans.
5) Transfer the risen dough to a lightly greased work surface, and pat or roll it into a 16" x 12" rectangle. Itâ€™s a nice, soft dough, and pats out easily.
6) To make the filling, whisk together the sugar, cinnamon, and flour.
7) Brush the dough lightly with milk.
8) Sprinkle the filling evenly over the dough, covering the entire surface.
9) Roll the dough into a log the long way; it'll stretch to about 20" long as you roll.
10) Using a serrated knife, slice the log into 16 slices. In order to cut down on drag, it helps to rinse the blade in hot water, and wipe it off, between slices.
11) Space eight rolls in each of the prepared pans. Flatten them gently.
12) Cover the pans, and let the rolls rise till they're noticeably puffy, about 1 1/2 to 2 hours; they should spread out and start to crowd one another.
13) While the rolls are rising, preheat the oven to 375°F.
14) Bake the rolls till they're brown around the edges and beginning to turn golden brown across the center, about 20 minutes.
15) If you're going to serve the rolls immediately, make the icing while the rolls are baking. Combine the sugar, vanilla, and enough cream or milk to make a spreadable icing. If you're not serving the rolls immediately, don't make the icing yet.
16) Remove the rolls from the oven, and loosen their edges with a knife. Turn them out of the pan onto a rack. To enjoy right away, spread with the icing and serve.
17) To serve the rolls later, allow them to cool completely, then wrap in plastic wrap and store at room temperature for up to 3 days. Fifteen minutes before you're ready to serve, preheat the oven to 350°F. Unwrap the rolls, place them on an ungreased baking sheet, and tent lightly with aluminum foil. Bake for 10 to 15 minutes, until they're nicely warmed.
18) While the rolls are reheating, make the icing.
19) Remove the rolls from the oven, and spread with the icing. Serve immediately.