In a large mixing bowl combine ½ cup of each kind of flour and the yeast. In a small saucepan, heat and stir the milk, granulated sugar, oil, and salt just until warm 120 degrees to 130 degrees F (49 to 54 degrees C). Add to flour mixture along with egg substitute. Beat with an electric mixer on low to medium speed for 30 seconds, scraping bowl constantly. Beat on high speed for 3 minutes. Using a wooden spoon, stir in as much of the remaining flour as you can.
On a lightly floured surface, knead in enough of the remaining flour to make a moderately stiff dough that is smooth and elastic (6 to 8 minutes total). Shape into a ball. Place in a lightly greased bowl; turn once to grease surface. Cover and let rise in a warm place until double in size (about 1 hour).
Punch dough down. Turn out onto a lightly floured surface. Cover and let rest for 10 minutes. Spray an 8 x 4 x 2-inch (20 x 10 x 5-cm) loaf pan with nonstick coating. Set aside. In a small mixing bowl, stir together brown sugar and cinnamon. Set aside. Roll dough into a 12 x 8-inch (30 x 20-cm) rectangle. Brush lightly with water. Sprinkle with the cinnamon mixture. Top with apple.
Starting from a short side, roll into a spiral. Seal edge and ends. Place, seam down, in prepared pan. Cover and let rise until nearly double in size (about 30 minutes). Bake in a 375 degree F (190 degree C.) oven for 25 to 30 minutes or until bread sounds hollow when tapped. (If necessary, cover loosely with foil during the last 10 to 15 minutes of baking to prevent overbrowning.) Remove from pan; cool on a wire rack.
If desired, stir together powdered sugar and enough apple juice or milk to make a drizzling consistency. Drizzle over top of loaf.
Make-Ahead Tip: Prepare and bake bread as directed. Do not drizzle with icing. Wrap loaves in heavy foil; freeze for up to one month. To serve, thaw loaves at room temperature. If desired, prepare icing and drizzle over loaves.
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