In a large bowl, combine the water, yeast, and maple syrup. Stir gently and let stand for 5 minutes, until lightly foamy.
Add the olive oil, whole wheat flour, all-purpose flour, and salt. Mix until a shaggy dough forms.
Knead by hand or with a mixer for 6–8 minutes, until the dough is smooth, elastic, and soft. The dough should feel supple and only slightly tacky, but not sticky.
Shape the dough into a ball and place it in a lightly oiled bowl. Cover and let rise in a warm place for 1 to 1 1/2 hours, until doubled in size.
Turn the dough onto a lightly floured surface and divide into 12 equal pieces. Shape each piece into a smooth ball.
Cover and let rest for 20–30 minutes. This rest allows the gluten to relax so the dough rolls out easily and puffs properly.
Lightly flour the surface and roll each ball into a round 6–7 inches wide, about 1/8 inch thick. Keep the thickness even to encourage proper pocket formation.
Preheat the oven to 450–480°F (230–250°C) with an empty baking sheet or pizza stone inside. The baking surface must be very hot for proper puffing.
Place the rolled pitas onto parchment paper and carefully transfer them onto the hot baking surface.
Bake for 4–6 minutes, until fully puffed and lightly golden. Do not overbake, as this will dry them out.
Remove from the oven and immediately stack the pitas. Cover with a clean towel to keep them soft and flexible.
Notes
Refrigerator: Store pita bread in an airtight container for up to 4 days.
Freezer: Freeze in a sealed bag for up to 2 months. Separate layers with parchment if needed.
To reheat: Warm briefly in a dry skillet or wrap in foil and heat in the oven until soft.