In a large bowl cream together shortening and 1/2 cup of the sugar. Add eggs, one at a time, beating well after each addition. Set aside.
Combine flour, baking powder, baking soda and salt; mix lightly. Gradually pour into shortening mixture; beating until blended. Stir in oats, cheese, pecans and the diced apple, mixing well after each addition. Gradually add milk, stirring until all the ingredients are just moistened.
Preheat oven to 375° F. Grease 12 muffin tins and fill each two-thirds full of batter.
In a shallow bowl combine remaining 1/4 cup sugar and cinnamon. Melt butter in a small saucepan over low heat; remove from heat.
Dip apple slices into butter; and then into cinnamon/sugar mixture. Press an apple slice into the top of each muffin. Sprinkle with any remaining cinnamon/sugar.
Bake for 25 minutes or until golden brown.Servings: 1 dozen muffins