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Combine water, milk, and flour in small saucepan and whisk until no lumps remain; cook over medium heat, whisking constantly, until whisk leaves lines on the bottom of the pan, a few minutes. Remove from heat and add the butter in pieces, stirring to melt; set aside. Mix the starter with the warm milk and eggs and add this to the remaining dough ingredients and stir together; let rest, covered, for 20 minutes (gives flour chance to absorb liquid, making it easier to knead). Knead dough (by hand, mixer, or bread machine) to make a smooth, elastic, somewhat sticky dough. Shape dough into a ball and let rest in a lightly-greased covered bowl for 60-90 minutes. Combine brown sugar and cinnamon (note: this mixture weighs 150 g.) Divide dough in half and, on a floured surface, and one piece at a time, shape into a rough rectangle. Roll out until about a 18 x 8 inch rectangle. Sprinkle half the filling on the dough and roll up starting at long edge. Cut log into 12 slices. Repeat with remaining rectangle. Place rolls in a greased 9 x 13 inch pan. Cover and refrigerate overnight (or let rise for 45-60 minutes). Let the rolls sit out for one hour before baking if refrigerated. Bake for 22-25 minutes, until they feel set (may be just barely browned). Stir together icing ingredients. Remove rolls from oven and spread with icing.