Mix the milk and water in a stand mixer bowl or a big basin, and then sprinkle the yeast on top. Give the yeast some time to dissolve—about five minutes.
Add the butter, egg, brown sugar, and sugar and stir until well combined. Combine the flour, bread flour, and salt in a small bowl. The yeast mixture should receive roughly half of the dry ingredients. Stir to incorporate. Add the remaining dry ingredients and knead the dough for about 7 minutes, using the dough hook attachment in the bowl. Add flour one tablespoon at a time until the dough pulls away from the bowl's edges and forms a small dough "tornado" around the dough hook if you see that your dough isn't pulling away from the sides of the bowl or is too wet.
After you've finished kneading the dough, put it in a sizable basin that has been lightly greased, and cover it tightly with plastic wrap so it can rise for about 1-1/2 hours.
After the dough has risen, divide it in half and dump it out onto a lightly dusted surface. Roll one half into a substantial rectangle measuring approximately 15cm by 55cm using a rolling pin. Spread the melted butter over the top after pouring it. Sprinkle the dough that has been greased with an even layer of the cinnamon-brown sugar mixture.
Roll the dough tightly from end to end, starting with one of the long ends, and crimp the sides to close. About 20 chunks of dough measuring 3cm each should be cut out and arranged spiral-up in a small muffin pan that has been lightly oiled. Apply the remaining dough to this procedure once more. Allow to rise again for about 40 minutes while covered with plastic wrap.
Set the oven to 180 degrees while you wait. Once the oven is hot, bake the rolls for 15 to 17 minutes, or until the sides are just beginning to turn golden and the internal temperature reaches 90 degrees. After removing from the oven, make your icing.