In a two-cup measuring vessel, combine ½ cup warm water with the sugar and active dry yeast. Stir gently and allow the mixture to rest for approximately 10 minutes, or until a foamy surface develops, indicating that the yeast is active.

In the bowl of a stand mixer fitted with the paddle attachment, combine the flour, salt, and olive oil. Create a well in the center. Pour in the yeast mixture along with 1¼ cups of warm water. Switch to the dough hook and knead on medium speed for 6 to 8 minutes, or until the dough becomes smooth and elastic.

Transfer the dough to a lightly oiled mixing bowl, cover with a clean towel or plastic wrap, and allow it to rise in a warm location for approximately 1½ hours, or until doubled in size.

Once risen, portion the dough into 12 equal-sized pieces (each roughly the size of a small orange). Roll each piece into a ball and place them on a rimmed baking sheet. Cover with a kitchen towel and let them rest for 30 minutes.

On a lightly floured surface, roll each dough ball into a circle approximately ¼ inch thick. Cover again with a towel and allow a second rise for 30 additional minutes.

Preheat the oven to 500°F. Carefully place the dough rounds directly onto the oven rack. Bake for 5 to 7 minutes, or until the pita breads puff up and begin to lightly brown. Remove promptly and allow to cool slightly before serving.