In a medium mixing bowl, combine water, oil, sugar, yeast, salt, and whole wheat flour with a wooden spoon until combined and smooth. Stir in all-purpose flour until the mixture comes together into a shaggy mass.
Using clean hands, knead the dough in the bowl for 10 minutes or until it becomes smooth and very elastic, adding only very small amounts of extra flour if dough is extremely sticky (see note). Alternatively, knead dough at low speed in a stand mixer fitted with the dough hook attachment until dough is very elastic and smooth, about 8 minutes.
Meanwhile, place a baking steel or 12-inch cast iron skillet on the top oven rack and preheat oven to 500°F (260°C). Line a plate with a large, clean kitchen towel and set aside.
Turn dough out onto a lightly floured work surface and form into a smooth ball. Lightly oil a clean mixing bowl and place dough inside, then rub oiled hands over the top of the dough. Cover bowl with a damp cloth and let rise in a warm place for 1 hour.
