To make the dough, sift the flour, salt, and baking powder together. Make a well in the center, add the water and oil to it and blend until the dough is smooth. Knead the dough on a lightly floured surface for 1 minute. Cover and allow it to sit for at least 30 minutes at room temperature.
Cut the broccoli rabe into 2-inch pieces and blanch in a large pot of boiling salted water for 4 minutes or until tender. Drain well in a colander. Place the olive oil in a skillet over medium-high and saute the garlic until golden. Add the broccoli rabe, red pepper flakes, and salt to taste. Saute for another 4 to 5 minutes. Remove all ingredients from the pan and allow to come to room temperature.
Divide the dough into eight equal portions, then roll them out on a lightly floured surface into 8-inch rounds. Warm a skillet over high heat until a drop of water evaporates immediately upon hitting the surface. Place the pieces of dough in the skillet, dry, cooking one side until they become firm and golden, which should take less than a minute. Flip them over, cook the other side, then transfer to a plate or cutting board or just fill it in the pan, fold it over and then remove to a plate to serve hot. While the piadine are still hot, place the broccoli mixture in the center of them, fold them over to form half-moon shapes.