In the bowl of a stand mixer fitted with the dough hook attachment, add flours. Whisk in sugar, salt, and cardamom. Add yeast, and whisk into flour mixture. With mixer on low speed, add water, milk, and egg. Increase speed to medium, and add softened butter. Beat until a smooth, elastic dough forms, about 15 minutes. Place dough in an oiled bowl, cover with plastic wrap, and allow to rise until doubled in size (this will take about an hour but it could be longer if your kitchen is cool).
On a floured workspace, roll dough into a rectangle of about 15x17 inches. using an offset spatula, spread Cinnamon Filling all over dough. Roll up in a tight spiral. (As you roll, pull toward you to create this tight spiral.) Push each end toward center to compress roll. Trim off messy ends, then cut roll into 12 equal slices. (dental floss works best for this - slide under the dough to where I want to cut, then bring across the two ends, up and over the dough, pulling it tight to cut through—just like a cheese wire.) Place buns, spiral side up, in a 13x9-inch (33x22-centimeter) baking pan, leaving a little space between each one. Allow to rise until buns are swollen and wobble slightly when touched, about 30 minutes.