In a large bowl or the bowl of a stand mixer fitted with a paddle attachment, add 1 cup of the flour, the 1/4 cup sugar, the yeast and the salt. Mix briefly to combine.
In a small saucepan (or in a measuring cup in the microwave), warm the milk, water and butter to 110F.
Gradually add the warm milk mixture to the flour mixture and mix to combine. Increase the speed of the mixer to medium speed and mix for 1 1/2 - 2 minutes. Add the egg and another 1/2 cup of flour and continue mixing at medium speed for another minute of two. Scrape off the paddle attachment and replace it with the kneading hook. Reduce the speed of the mixer to low and begin adding more flour in very small increments, kneading well as you go, until you have a smooth, moist dough.
Remove the dough to a floured surface and knead by hand about 1 minute. Form into a ball, cover and let rest on a floured surface for 10 minutes.
Meanwhile, prepare the filling by stirring together the brown sugar and cinnamon. Set aside. Melt the 2 Tbsp butter for the filling and set aside. Prepare one large baking sheet by lining with parchment paper. Set aside.
After 10 minutes, roll the dough into a rectangle about 8x16-inch rectangle. Brush the dough with the melted butter, then sprinkle the brown sugar/cinnamon mixture evenly over-top. Fold the dough in half lengthwise, folding from the short (8") side. Gently roll the rectangle to flatten and widen to about 10-inches wide. Using a sharp knife or pizza cutter, cut the dough into ten strips, each 1-inch wide.
Shape the twists by taking a strip of dough and twist it 2-3 times. Place onto prepared baking sheet. Repeat with remaining dough strips, placing on the baking sheet with some space in between. Cover the baking sheet with plastic wrap and place into the refrigerator to rise for 2 - 24 hours.
When ready to bake, remove the twists from the refrigerator and uncover. Preheat oven to 375F. Let twists stand at room temperature for 10 minutes while your oven preheats.
Place twists in the oven and bake until set and golden, about 13-17 minutes. Remove from the oven and immediately transfer to a cooling rack to cool.
Serve dusted with icing sugar, or make a quick icing sugar glaze with 1/2 cup icing/confectioners' sugar, mixed with 1 1/2-2 tsp milk and mixing until smooth. Drizzle over cinnamon twists once they have cooled slightly (or the icing will melt right off :).
You can use either Instant or Dry Active Yeast for these, in place of the Rapid or Quick Rising Yeast, however, instead of the 10 minutes rest, you will need to do a full first rise at room temperature until the dough doubles in size. Additionally, you may want to extend the minimum refrigeration time from 2 hours, to 3 or 4 hours.Be sure to read the Tips section above the recipe card for more tips on making these.