Special equipment: 3-inch cookie cutters in assorted shapes, such as animals, stars and flowers
Place an oven rack in the center of the oven. Preheat the oven to 375 degrees F. Line a baking sheet with parchment paper.
Crumble the oregano and salt in a small bowl using your hands and set aside.
Combine the flour, baking powder and butter in a food processor. Pulse until the mixture forms a coarse meal. Add the cheese and 1 tablespoon ice water. Process until the mixture forms into a ball, adding extra water, 1 teaspoon at a time, if needed. On a lightly-floured work surface, roll out the dough into a 10-inch-diameter circle, about 1/4-inch thick. Form the dough into a flat disc and cover with plastic wrap. Refrigerate for 30 minutes.
Sprinkle the dough with the seasoned salt. Gently roll the salt into the dough using a rolling pin.
Cut the dough into different shapes using the cookie cutters, and transfer to the prepared baking sheets. Bake until puffed and golden, 10 to 12 minutes. Transfer to a wire rack to cool, about 10 minutes.