In the bowl of a stand mixer, combine bread flour, whole wheat flour, and water.
Stir together just until mixed.
Cover and let stand for 30 minutes.
Switch to dough hook, if using.
Add sourdough starter and salt.
Mix on low speed until incorporated, about 1-2 minutes.
Increase speed to medium.
Knead for 3-4 minutes. (Dough temperature should be 76 degrees F.)
Reduce speed to low.
Mix in figs and walnuts.
Turn into a medium glass bowl.
Cover with plastic wrap.
Proof at a warm room temperature (76 degrees) for 1 hour.
Turn dough by folding each of the 4 sides toward the middle.
Turn over so that folds are on the bottom.
Continue proofing for another 1-1 1/2 hours, until puffy but not completely doubled in bulk.
Line a banneton with a tea towel.
Sprinkle bottom and sides with rice flour. Set aside.
Turn dough out onto a lightly floured surface.
Turn dough vertically.
Press out lightly into a rectangle.
Fold the top third of the dough toward you.
Fold in both the left and right corners.
Roll the folded part toward you, forming a cylinder.
Seal gently.
Place thumbs on top of cylinder and roll toward you until your thumbs touch the flat part of the dough.
Push in slightly to tighten the dough.
Repeat process until dough is completely rolled.
Roll gently to seal seam.
Place seam side up in prepared banneton.
Cover.
Proof at warm room temperature (76 degrees) for 1 1/2-2 hours.
While dough is proofing, place a baking stone in the center of the oven.
Place a sheet pan on bottom rack.
Heat oven to 450 degrees F.
Turn dough out onto a piece of parchment paper.
Use a lame or a sharp knife to score the bread.
Using a peel (or the back of a sheet pan), slide the loaf onto the hot stone.
Pour at least 2 cups of water into the preheated sheet pan.
Close the oven.
Bake for 15 minutes.
Reduce oven temperature to 425 degrees. (Do NOT open oven door.)
Continue baking for an additional 20 minutes.
Remove to a cooling rack.
Allow to cool before slicing.