Combine 2 cups flour, sugar, salt and dry yeast in a large mixer bowl.Heat milk and butter until warm (100˚F to 110˚F). Add milk mixture and eggs; beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Stir in the remaining flour, 1 cup at a time, to make a soft dough.
Knead on lightly floured surface until smooth and elastic, about 5 minutes. Place in a greased bowl, turning to coat. Cover with a clean towel and let rise in a warm, draft-free place about 1 hour, or until doubled in size.
Filling: Mix brown sugar, sugar, flour and cinnamon in a small bowl. Using a pastry blender or two knives, cut butter into sugar mixture until the mixture resembles coarse crumbs. Set the chopped apple and peanuts aside until you are ready to sprinkle them on the filling.
Caramel Syrup: Place butter, brown sugar and corn syrup in a saucepan. Cook over medium heat, stirring constantly, until sugar dissolves. Pour Caramel Syrup into a lightly greased 13 x 9-inch baking pan AND either a 9 x 9-inch pan OR a 9-inch round cake pan.
Punch down dough and divide in half. Roll out one portion of dough on a lightly floured surface to a rectangle about 15 x 10 inches. Sprinkle half of the Filling over dough; top with half of the chopped apple and peanuts. Starting from the long side, roll up jelly-roll style. Pinch the edges to seal. Brush edges of dough with some milk if you have trouble getting the dough to seal.
Using a very sharp knife, cut the dough into 9 pieces. Place pieces, cut-side down, on syrup in pans. 12 rolls will go in 13 x 9-inch pan and 6 in the 9-inch pan. Repeat with remaining dough. Cover and let rise 30 to 45 minutes, or until nearly doubled.
While rolls are rising, preheat oven to 350˚F. Bake rolls 40 to 45 minutes, or until lightly browned. While they are still warm, invert onto a serving plate.
* Substitute pecans for peanuts, if desired.