In a mixing bowl, whisk together the yeast and warm water. Let stand and bloom for about 20 minutes. Mix on low speed, the flour, cold water, olive oil, and salt. Beat in slowly at first and then increase the speed of the mixer as the flour in incorporated. Turn the speed down and mix until the dough becomes soft and begins to pull away from the sides of the bowl. Pour it out on a floured board. Knead the dough adding flour to dust as needed. Shape the dough into a large ball and cover with a towel to let stand until it doubles in size, about 1 hour.
Heat a saute pan with 2 tablespoons of olive oil and add the leeks. Turn the heat to medium high and sweat the leeks until soft and translucent. Set aside and let cool. When ready, cut the dough into 6 ounce pieces. Roll it out to about 1/2-inch thick circle a little smaller than the skillet. Heat a large skillet with the remaining 2 tablespoons of olive oil. Place the rolled dough into the skillet and flip it to brown on both sides. Once browned, sprinkle the top with feta cheese, leeks, 1 teaspoon salt, and pepper. Bake in a preheat 350 degree F. oven just long enough for the cheese to melt. Pull from the oven and cut into 6 pieces. Serve warm.