DOUGH:In the bowl of an electric mixer, combine yeast with warm water and 1 teaspoon of sugar and let sit for 5 minutes until foamy. Add egg, sugar, butter, salt and the bread flour. With the paddle attachment, mix on medium speed for 1 minute until smooth. Gradually add the whole wheat flour, mixing until a soft dough forms.
Turn out onto a lightly floured surface and knead adding additional bread flour if sticky. When it is smooth and elastic, place in a lightly greased bowl and cover with plastic. Place in a warm place and let rise until doubled, 45 minutes.
FILLING: While the dough is rising prepare the filling. Add 1 tablespoon butter to a skillet over medium-high heat. Add diced apples, raisins and brown sugar and cook for 5 minutes, until apples are crisp-tender, not mushy. Let cool for 30 minutes.
Punch down dough and place on a lightly floured surface. Roll into a 20 x 12 inch rectangle. Spread softened butter over the dough. Combine sugar and cinnamon and sprinkle over the butter. Next add the apple mixture and sprinkle with pecans.
Cut dough into 5 strips that are 12 x 4 inches each. Carefully place each strip on top of each other replacing apple mixture as you go. Cut the strip into 6 even rectangles and then cut each rectangle in half so that you end up with 12 stacks. Place each in a muffin tin with the cut side facing up.
Cover loosely and let rise for 45 minutes until the rolls are about 3/4 inch above the muffin tin.
Preheat oven to 375º. Place a baking sheet under the muffin tin in case it drips. Bake until golden brown, about 15 minutes. Remove to a wire rack and let cool slightly before removing. Serve with butter or cream cheese frosting.
FROSTING: In a small bowl, creme butter and cream cheese. Add powdered sugar, vanilla, salt and caramel and beat until smooth. Add milk until it’s the consistency you want.