Combine the yeast and water in the bowl of a stand mixer and stir well. Add ¼ cup of the bread flour and let sit for 10 minutes. Bubbles should form to let you know the yeast is working.
Stir the honey and oil into the yeast mixture; add salt, whole wheat flour and rye flour (and vital wheat gluten, if using) and stir well. Dough should be very sticky at this point. Add another ¼ cup of bread flour and stir – now dough should be a little bit dryer, but still a tad bit sticky. At this point you should still have ¼ cup of bread flour left to control stickiness. If dough is still really sticky, go ahead and add 2 tablespoons more. The dough will be kind of a dense one, yet it shouldn't feel dry.
Put the bowl on the stand mixer, attach the dough hook and let the mixer knead until smooth and elastic. If dough clears the side of the bowl as it kneads, continue kneading without adding remaining flour. If it does not, go ahead and add remaining 2 tablespoons of flour.
If you weighed your flour, you'll probably use ALL the bread flour.
Put about ½ tablespoon of extra olive oil or walnut oil in another mixing bowl. Set the kneaded dough in the bowl and turn it to coat the dough ball with oil. Cover with plastic wrap and set in a warm place (like a closed microwave) for an hour to 1 ½ hours or until doubled in bulk.
Punch dough down and knead in the walnuts. Shape into a ball, set the ball on a parchment lined baking sheet, cover with up upside down mixing bowl and let rise for another 45 minutes.
When dough has risen, use a razor blade to make an x through the top – do it carefully without deflating the dough too much. Brush lightly with egg white if desired and bake at 375 degrees F for 25 to 30 minutes or until dough sounds hollow when tapped. Let cool completely and slice (or serve hot – it slices neatly when cool). Alternatively, bake it for 15 minutes at 450 in a preheated, covered Dutch oven. Remove top and bake for another 20 minutes at 350.
Notes
If during your second rise, your dough spreads outward rather than rises upward, gently smooth the sides downward, tucking them under gently and plumping the shape into a ball that is taller than it is wide. Do this a couple of times, gently so as not to lose height, and allow the dough to rise for another 10 minutes.