In a large bowl, combine the flour, salt, and baking powder, and whisk to incorporate.
Using a rubber spatula, make a well in the center of the flour and pour in the water and oil. Fold the liquids into the flour until a shaggy dough forms.
Turn the dough out onto a lightly floured counter and knead with the heels of your palms until the dough forms a smooth ball, about 3 minutes; if the dough feels too sticky, incorporate in more flour.
Loosely drape a kitchen towel over the dough and allow it to rest for at least 15 minutes, or up to 1 hour.
Divide the dough into 16 equal portions. Working with 1 piece at a time, roll a portion into a ball between your palms, then lightly toss in extra flour, making sure to shake off any excess. Using a rolling pin, roll the ball out into a thin disc; if the dough is sticking to the pin, dust the pin with flour.
Heat a heavy-bottomed pan (like a cast-iron skillet or Dutch oven) over high heat. Add a tortilla and cook until large bubbles and a few dark spots form, about 1 minute. Flip and brown the other side, 30 seconds to 1 minute. Transfer to a clean kitchen towel and fold it over to keep the tortillas from drying out.
Continue rolling and cooking, and stacking the tortillas in the towel. Serve immediately.