Add 1 cup of lukewarm (100 - 120F) water into a mixing bowl. Add yeast and sugar, and stir to dissolve. Tip in the whole-wheat flour and 1/4 cup of the all-purpose flour and mix.

Leave the mixture in a warm part of your kitchen until it is frothy, 15-20 minutes.

Add 1 3/4 cups of the remaining all-purpose flour (you'll have 1/2 cup left for dusting) as well as the salt and olive oil. Stir with a wooden spoon until you have a rough mixture. Dust with a little reserved flour, then knead for a minute.

Turn the dough onto a work surface and knead further for a couple of minutes. Cover and let it rest for 10 minutes, then knead again for 2 minutes. Add a little more flour only if the dough seems too wet. Return the dough to the bowl, cover tightly with plastic wrap, and leave in a warm place until dough has doubled in size, about 1 hour.

On the bottom shelf of a cold oven, place a cast-iron pan, griddle or pizza stone, and preheat to 475F / 250C. Meanwhile, punch down dough and divide into 8 pieces of equal size. Form each piece into a little ball. Place dough balls on work surface, cover with a damp towel and leave for 10 minutes.

Remove 1 ball (keeping others covered) and press into a flat disk with rolling pin. Roll to an 8-inch diameter, about 1/8 inch thick.

Carefully lift the dough circle (you may wish to use a large pastry cutter) and place quickly on the hot baking sheet in the oven. After 2 minutes the dough should be nicely puffed. Turn over with tongs or spatula and bake 1 minute more. The pita should be pale, with only a few brown speckles. Transfer warm pita to a napkin-lined basket and cover so bread stays soft. Repeat with the rest of the dough balls.