Step 1

In a large bowl, whisk together flour, yeast, sugar and salt. Set aside.

Step 2

In a medium microwave-safe bowl, combine milk and shortening. Warm in 5-second increments in the microwave (or on the stovetop), just until the mixture is lukewarm (about 110 degrees F) and the shortening is melted. If the liquid gets hotter than 110 degrees F, just let it sit on the counter for a few minutes to cool. You want it to feel like warm bath water.

Step 3

Pour the warm milk mixture into the dry ingredients and stir. Add the egg; mix until a soft dough comes together. Add more flour (1 tablespoons at a time), if necessary, until the dough pulls away from the sides of the bowl. It should be slightly sticky, but not sticking to the sides and bottom of the bowl. Knead for 5 minutes.

Step 4

Transfer dough to a large greased bowl; turn the dough so that it’s greased on all sides. Cover with a clean towel or plastic wrap. Let rise in a warm spot until doubled in size, about 2 hours.

Step 5

Combine brown sugar and cinnamon in a small bowl. Set aside.

Step 6

Turn dough out onto a floured surface. Roll dough into a long rectangular shape about 8 inches x 14 inches. Spread softened butter on top. Sprinkle with the brown sugar mixture. Starting on one of the long sides, roll up the dough into a tight cylinder; pinch lightly to seal the seam. Slice into 8-10 even rounds. Transfer the pieces, cut-side up, to a greased 9-inch round cake pan or 9-inch square baking dish.

Step 7

Cover and let rise in a warm spot until puffy, about 1 hour. Remove cover.

Step 8

Bake in a 350 degree F oven for 25-35 minutes, until the buns are a deep golden brown and the insides are cooked through. If the tops start to get too dark before the dough is fully cooked, tent loosely with foil. Transfer to a wire cooling rack; prepare glaze.

Step 9

Use a whisk or electric mixer to combine all of the glaze ingredients in a medium bowl until smooth. It should be quite thick. Spread about ½ cup of the glaze on top of the warm buns. Let the buns cool for about 10 more minutes. Spread the remaining glaze on the warm buns and serve.