In a large bowl, combine one egg, one-half cup of plain Greek yogurt, and two-thirds of a cup of heavy cream. Mix until well combined and smooth.
In a separate bowl, sift together one cup of Bisquick, two tablespoons of granulated sugar, and one-half teaspoon of cinnamon.
Mix the wet and dry ingredients together, then add one-quarter teaspoon of vanilla extract and continue mixing until well combined. Fold in the grated apple. Set aside while preparing the caramel sauce.
To prepare the caramel sauce, combine one cup of brown sugar, one-half cup of heavy cream, five tablespoons of unsalted butter, and one-eighth of a teaspoon of salt in a small saucepan. Bring to a boil over medium-high heat, occasionally stirring for five minutes. The mixture should appear bubbly. Add one teaspoon of vanilla extract and continue stirring for two minutes. Remove from heat and allow to cool before using or transferring to a glass storage container.
Lightly grease a skillet and place over medium heat. Using a measuring cup, scoop one-third of the batter for each pancake and cook until each side is lightly browned. (Flip when bubbles appear on the surface).
Serve with a caramel sauce, or powdered sugar and maple syrup, if desired.