Fit your dough hook into your stand mixer.
Whisk the whole wheat flour, all-purpose flour, salt, pepper, and yeast in a bowl fitted into your stand mixer.
Combine olive oil and warm water in a pitcher, then pour into the flour mixture. Turn on the mixer and let the dough hook knead for 5 minutes, until dough has formed a tight ball around the hook.
While the dough is kneading, pour about 1 tbsp olive oil into a large bowl and lightly spread it around the interior with a paper towl. You want the entire interior of the bowl oiled.
Lightly wet a kitchen handtowel, wringing out all excess water until the towel is damp.
When the five minutes are up, turn off mixer and remove the dough from the hook. The dough will be smooth, not sticky, and slightly warm to the touch.
Place the dough into the oiled bowl, then cover with the damp towel. Place bowl in a warm place and let rise for about an hour until dough is doubled in size.
While you're waiting for the dough to rise, chop your figs and set aside.
Place about 1/4 cup of all-purpose flour in a small bowl and set aside.
Once the hour has passed, remove the dough from the bowl and place on your workspace. Lightly flour your hands with the flour you set aside (while keeping some in reserve), then gently knead the chopped figs into the dough. Be sure to incorporate the figs evenly throughout the dough to make sure they don't all end up on the crust.
Note: this is a messy process since the fresh figs are juicy. Re-flour your hands as necessary.
Once figs are incorporated, place dough on an ungreased baking sheet and shape into an oval. Using a sharp knife, slice three shallow lines along the top of the dough, then spinkle all over with flour.
Let the dough rise, uncovered, on the baking sheet for another 10-15 minutes until it's poofed up. It make take a bit longer if your kitchen isn't warm.
Preheat your oven to 350F.