Mix the yeast and the warm water and let stand for 5-10 minutes or until the yeast is all bubbly and happy.
Add the sourdough starter, mix it well with the yeast, then add the whole-wheat flour and the vital wheat gluten.
In a stand mixer set to low speed or by hand, mix everything. Then slowly, a little at a time, add the bread flour until you have a dough that's not sticky. I needed just about 3/4th of a cup. You might need less or more.
Continue kneading by hand or in the stand mixer for 10 minutes. You should have a very beautiful, resilient, elastic dough.
Form the dough into a smooth ball. Spray oil to coat a large bowl, place the dough, top side down, in it, and turn over once so the top is coated in oil.
Cover with a kitchen towel and let it rise in a warm place for about two hours or until it has doubled in size.
Once it has doubled, punch down the dough to get all the gases out. Then divide into two, shape into balls, and let them rest on the countertop, covered, another 10 minutes.
Follow the shaping techniques in this step-by-step recipe post
to form two baguettes.
Place the baguettes on a baking sheet dusted with cornmeal, at least three inches apart. Dust them with some flour, cover loosely with a kitchen towel, and let them rise in a warm place for another hour.
Start preheating your oven to 425 degrees about half an hour before baking your bread. Place a pan in the bottom rack of the oven.
When you are ready to put the loaves into the oven, take a sharp knife or blade and score each loaf three times. The cuts should be diagonal and should be parallel to each other.
Just before you put the loaves in the oven, pour a cup of water in the pan you placed in the bottom rack. Then place the baking sheet in the oven and bake 30-35 minutes or until the loaves sound hollow when tapped on the bottom.
Remove the loaves to a baking rack to cool.