For the rolls: Dissolve the yeast and 1 teaspoon of the sugar in 3/4 cup warm water. Let stand for 10 minutes until the mixture becomes bubbly.
In a large bowl, stir together the remaining 3/4 cup sugar, the milk, shortening and egg. Using a wooden spoon, mix in the flour until the dough comes together and pulls away from side of the bowl. Pour the dough out onto a floured cutting board and knead for about 5 minutes.
Place the dough into a greased bowl, cover with plastic wrap, and then store in a warm place until doubled in size, about 1 hour.
For the filling: Meanwhile, in a small bowl, mix together the sugar and cinnamon, and then set aside for later use.
Punch the dough down and turn out onto a floured cutting board. Cut the dough in half and use a rolling pin to roll into two 1/4-inch-thick rectangles. Spread 2 tablespoons of the margarine over each rectangle of dough. Sprinkle half of the cinnamon sugar onto each rectangle of dough, then, starting on the long side, roll the pieces of dough into logs and cut in 1-inch slices.
Place the rolls onto a baking sheet 1-inch apart and press them down slightly. Place the baking sheet in a warm place to proof until doubled in size, 30 minutes.
Preheat the oven to 350 degrees F.
Bake the cinnamon rolls for 30 minutes. Cool the rolls slightly.
For the frosting: Using an electric mixer, mix the confectioner's sugar, margarine and vanilla extract until smooth. Add the milk until the frosting reaches a runny consistency.
Pour the frosting over the cinnamon buns and serve.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.