In a medium skillet or saucepan, combine apples, butter, granulated sugar, lemon juice, corn starch, and cinnamon. Heat on medium-high heat until bubbly; reduce heat and simmer 5 minutes until thickened.
Cut crusts off of 12 slices of Martin's Potato Bread. Use a rolling pin to roll bread as flat as you can; trim as necessary to make a square.
Spoon 1-2 Tbsp. apple pie filling onto each piece of bread.
Divide Brie cheese into 12 pieces and add 1 piece to each turnover.
Fold bread into a triangle; use a fork to seal edges closed. Brush both sides of turnovers with 1 beaten egg combined with 1 tsp. water.
Place turnovers on a baking sheet. Sprinkle with sugar and bake at 400° for 12-15 minutes.
Remove from oven. Drizzle with a combination of 1/2 c. powdered sugar, 2 1/2 tsp. milk, and 1/8 tsp. cinnamon.