In a large mixing bowl, combine the sourdough discard, flour, salt, and baking powder. Stir with a spoon or spatula until a shaggy dough forms.
Add the 2 tablespoons of olive oil and 1/4 cup of water (or milk). Mix until a cohesive dough comes together. If the dough feels too dry, add more water, a tablespoon at a time, until it’s soft and slightly sticky but manageable.
Turn the dough out onto a lightly floured surface. Knead gently for 2-3 minutes until it’s smooth. The dough should be soft and pliable.
Divide the dough into 4 equal portions. Roll each portion into a ball.
Working with one ball at a time on a lightly floured surface, use a rolling pin to roll out the dough into a thin, rustic circle or oval, about 6-8 inches in diameter. Don't worry if it's not perfectly round; rustic charm is part of the appeal!
Heat a tablespoon of olive oil in a cast iron skillet or other heavy-bottomed pan over medium-high heat. Once the oil is shimmering, carefully place one flatbread into the hot skillet.
Cook for 2-3 minutes per side, until golden brown and puffed in spots, with crispy edges. You may need to adjust the heat to prevent burning.
Remove the cooked flatbread from the skillet and place it on a plate. Repeat with the remaining dough portions, adding more olive oil to the skillet as needed between batches.
Serve immediately with your favorite toppings.