In the bowl of a stand mixer fitted with the dough hook attachment, add the flours.
Whisk in the sugar, salt and cardamon.
Add yeast and whisk into the flour mixture.
Turn the mixer on low speed, and add the water, milk and egg.
Increase the speed to medium and add softened butter.
Beat until a smooth, elastic dough forms, about 5 minutes. (You can do this by hand, too, but it takes about 15 to 20 minutes of kneading).
Place dough in an oiled bowl and cover with plastic wrap and let rise until doubled in size, usually an hour and a half to 2 hours, but could take longer.
On a floured work area, roll the dough into a rectangle about 15 inches long and 10 inches wide.
Spread the melted butter (1 stick) over the dough.
Sprinkle the sugar and then the cinnamon over the butter.
Beginning on the long side, roll up the dough completely, and gently pinch the edge together to seal.
Cut 12 to 15 slices from the rolled dough.
Coat the bottom of a baking dish with butter and sprinkle with sugar
Place the rolls in the pan and let rise until almost doubled, about another hour.
Pre-heat oven to 350° F.
Bake for 25 minutes, or until lightly browned on top.
Let rolls cool for at least 5 minutes.
Meanwhile, mix melted butter (4 tablespoons), powdered sugar and vanilla.
Add hot water, 1 tablespoon at at time, until the glaze reaches a smooth consistency.
Using a spoon, pour icing over the tops of the warm rolls.