1. Prepare Dough: Combine first 3 ingredients in bowl of a heavy-duty electric stand mixer; let stand 5 minutes. Stir in egg, next 3 ingredients, and 1 1/2 cups bread flour. Beat at medium speed, using paddle attachment, 1 minute or until smooth. Gradually beat in whole wheat flour and enough remaining bread flour to make a soft dough.
2. Turn dough out onto a well-floured surface, and knead until smooth and elastic (6 to 8 minutes), sprinkling surface with bread flour as needed. Place dough in a lightly greased large bowl, turning to grease top. Cover with plastic wrap, and let rise in a warm place (85º), free from drafts, 45 to 55 minutes or until doubled in bulk.
3. Meanwhile, prepare Filling: Melt 1 Tbsp. butter in a large skillet over medium-high heat. Add apples and next 2 ingredients, and sauté 4 to 5 minutes or until apples are crisp-tender. Cool completely (about 30 minutes).
4. Punch dough down; turn out onto a lightly floured surface. Roll into a 20- x 12-inch rectangle. Spread remaining 8 Tbsp. softened butter over dough. Stir together 3/4 cup granulated sugar and cinnamon; sprinkle over butter, and top with pecans and apple mixture.
5. Cut dough into 5 (12- x 4-inch) strips; stack dough strips. Replace any apples and pecans that fall out. Cut stack into 6 (4- x 2-inch) rectangles; cut each rectangle in half crosswise to form 12 (2-inch) squares. Place stacked squares, cut sides up, into cups of a lightly greased 12-cup muffin pan. Cover loosely with plastic wrap; let rise in a warm place (85º), free from drafts, 45 minutes to 1 hour or until rolls rise about 3/4 inch above rim of pan.
6. Preheat oven to 375º. Bake 18 to 20 minutes or until deep golden brown. Cool in pan on a wire rack 5 minutes. Remove from pan to a wire rack.
7. Prepare Glaze: Bring 1/3 cup butter and 1/3 cup brown sugar to a boil in a 1-qt. heavy saucepan over medium heat, stirring constantly; boil 1 minute, stirring constantly. Remove from heat; drizzle over top of warm rolls.