In stand mixer bowl, add 1 cup bread flour, yeast, salt, flax and sesame seeds; mix well. Add warm water, molasses and oil to flour mixture. Using a paddle attachment, blend on low speed for 30 seconds; beat on medium speed for 3 minutes. Add egg; beat 1 minute.
Switch to dough hook attachment. Gradually stir in whole wheat flour and enough remaining bread flour to make a firm dough. Knead until smooth and elastic, about 5 to 7 minutes.(NOTE: For hand mixing: following above steps, mix ingredients in large mixing bowl using a wooden spoon or dough whisk. Knead on floured surface until smooth and elastic.)
Place dough in lightly oiled bowl and turn to grease top. Cover; let rise until indentation remains after poking dough with finger down to second knuckle, about 1 hour.
Prepare pan: Grease a 9x5-inch bread pan; set aside.
Turn dough onto lightly floured surface; punch down to remove air bubbles. Roll or pat into a 14x7-inch rectangle. Starting with shorter side, roll up tightly, pressing dough into roll. Pinch edges and taper ends to seal. Place in prepared pan, seam side down. Cover; let rise until indentation remains after touching.
Preheat oven to 375°F.
Bake for 30 to 40 minutes. Remove from pan; cool on wire rack.