In the bowl of an electric mixer fitted with the dough hook attachment place the whole-wheat flour, all-purpose flour, yeast, salt, and sugar. With the mixer on low speed, gradually add the oil and 1 1/3 cup lukewarm water. Knead on low speed until the dough is firm and smooth, about 10 minutes.
Divide the dough into 4 balls, about 7 1/2 ounces each. Line 2 baking sheets with parchment paper. Place 2 balls on each sheet and cover with a damp towel. Allow the dough to rise in a warm spot until they have doubled in size, about 2 hours.
To roll out the dough; dab your fingers in flour and then place 1 ball on a generously floured work surface. Press down the center of each ball with the tips of your fingers, stretching the dough out with your hand. When the dough has doubled in width, using a floured rolling pin, roll the dough out until it is very thin, like a flatbread. The outer border should be slightly thicker than the center. Transfer the dough with a spatula or the back of a knife, allowing it to fold up almost like an umbrella, to a paddle. Do not worry that the pizza is not round, you are looking for an 8 to 10-inch shape, a cross between an oval and a rectangle. If you get a hole, simply pinch the edges back together. Repeat with the remaining balls.
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