Pour ½ cup water into a small saucepan. Add ⅓ cup flour and whisk. Add ½ cup milk and whisk until smooth with no lumps.Heat over medium heat until smooth and thickened like a slurry.Remove from heat and cover with plastic wrap to cool. Press wrap against the mixture to prevent scum from forming.
Dough
Place ½ cup warm milk in a large mixing bowl. Add 1 teaspoon of sugar to the milk and stir. Sprinkle the yeast over the mixture and stir until dissolved. Allow the mixture to sit for approximately 15 minutes to allow the yeast to bloom. The mixture will be bubbly when it is ready.
Once the yeast mixture is ready, add the milk bread starter to it along with the remainder of the sugar, egg, flour, salt, and butter. Mix by hand until combined.
Using a dough hook, knead the dough for 2-3 minutes at LOW speed. Turn the speed to medium and knead until the dough forms a smooth ball.
Place the dough in a greased/oiled bowl, turning once oil the top. Cover with plastic wrap and allow it to rise in a warm place until doubled, approximately 1 to 1.5 hours.
Roll the dough into a large rectangle. Spread rectangle with softened butter.
Combine cinnamon and sugar and sprinkle over the buttered rectangle.
Starting at the long end, roll each rectangle into a log, gently pulling backward during the process to help the roll stay tight. Pinch the seams together to seal. Cut into twelve slices and place in a 9x13 baking pan that has been sprayed with non-stick cooking spray.Cover the pan and let rise until doubled in a warm place, about an hour.
Preheat oven to 350 degrees Fahrenheit.
Microwave heavy whipping cream on HIGH for 20 seconds. Stir and then spoon cream on top of cinnamon rolls.
Bake rolls on the center rack of the oven for 30-35 minutes or until golden brown. Remove from the oven and allow to cool in the pan for 20 minutes.
Spoon or pour icing over the tops of the rolls while still slightly warm.
Glaze/Icing
Combine the powdered sugar, sour cream, and vanilla and mix until smooth.