In the bowl of a food processor, combine the flour, baking powder, 1/2 teaspoon salt, and chives and process for 5 seconds to combine. Add the shortening and process until well combined, about 15 seconds. Add the milk and 2 tablespoons water. Process to bring the dough together.
Remove from the processor and knead 1 minute to form a ball. Cover with plastic wrap and set aside for 30 minutes.
Heat a cast-iron skillet until very hot. Divide the dough into 3 pieces and form each into a ball. On a lightly floured surface, roll out the dough in a 6 1/2-inch-diameter circle to less than 1/16 inch thick. Prick the dough with a fork, brush with the olive oil, and sprinkle with the kosher salt. Transfer the round of dough, with the oiled side down, to the hot skillet and reduce the heat to medium. Cook about 1 to 2 minutes on each side, until the surface is covered with golden to dark brown speckles. Remove the bread from the skillet and transfer to a baking sheet in a warm oven.
Repeat the rolling and cooking process with the remaining dough. Cut the bread into wedges with a pizza wheel or sharp knife and serve.