Melt butter. In a bowl, dissolve yeast in warm water. Add buttermilk, melted butter, 6 Tbsp sugar, 1 tsp cinnamon, 1 egg, and whole wheat flour. Stir to blend. Add the all-purpose flour. Knead dough until smooth and elastic, then let rise in a warm place for about 40 minutes. Punch down. Peel apples and cut them into wedges. On a floured board, knead dough until satiny. Divide into 3 parts. Roll each out into a rectangle. Cut each rectangle into 10 squares. Place one apple wedge in the middle of each square. Combine remaining sugar and cinnamon. Sprinkle mixture over apple wedges. Fold dough over apples to cover completely. Place rolls on a greased baking sheet, seam-side down. Brush with beaten egg, then sprinkle with sesame seed. Bake at 400 for about 8 minutes. Increase temperature to 425 and bake for another 4 minutes until golden brown. Cover and cool on a wire rack.
FREEZING: These apple rolls freeze well. Wrap in small batches. Thaw before re-heating at 350.