Pigs in a Blanket with Homemade Dough

Ingredients (10)

• 1 package (1/4 ounce) active dry yeast
• 1/3 cup plus 1 teaspoon sugar, divided
• 2/3 cup warm milk (110° to 115°)
• 1/3 cup warm water (110° to 115°)
• 1 egg, beaten
• 2 tablespoons plus 2 teaspoons shortening, melted
• 1 teaspoon salt
• 3-2/3 cups all-purpose flour
• 10 hot dogs
• 2 slices process American cheese