Combine the water and yeast in the bowl of an electric mixer fitted with the dough hook. Let sit for about 5 minutes, until foamy. Add the flour, salt, and olive oil and mix on low speed for 1 to 2 minutes, until the flour is fully incorporated. Increase the mixer speed to medium and mix for 3 to 4 minutes, until the dough forms a smooth ball. Transfer the dough to a lightly oiled bowl and cover with a clean dish towel. Let rise for about 1½ hours, until doubled in volume.
Transfer the dough to a lightly floured work surface and divide into 8 equal pieces. Roll each piece of dough into a thin 8-inch circle. Cover the pitas with the dish towel while you work.
Heat a few teaspoons of vegetable oil in a large cast-iron skillet over medium-high heat. Add one pita to the pan and cook for 1 to 2 minutes per side, until golden brown and charred on both sides. Repeat with the remaining pitas, adding more oil as needed.
Stir together the oregano, garlic, salt, and pepper in a small bowl to combine. While the pitas are still warm, sprinkle the spice mixture over the tops.