In a medium bowl, stir the flour, salt, and baking powder. Add the shortening or lard and cut it into the flour with a pastry blender or two table knives until the mixture resembles a coarse meal. Stir in 2/3 cup warm water with a fork until a shaggy dough forms. Turn the dough out onto a floured surface and knead until smooth and soft, 3 to 4 min., reflouring the surface as necessary. After kneading, the dough shouldn’t be very sticky.
Make the dough.
Portion the dough into eight equal pieces (about 2 ounces each) and shape each piece into a ball. Cover the dough balls loosely with plastic and let rest on the counter for at least 30 min. and up to 2 hours.
Form the dough into balls.
When ready to cook the tortillas, heat a large (11- to 12-inch) dry cast-iron skillet or griddle over medium heat until hot. Working with one ball of dough at a time (keep the remaining dough covered) and using just enough flour to prevent sticking, roll the dough into a 9- to 10-inch round. The dough should be so thin that you can vaguely see the pattern of your countertop through it, and it should be more or less circular, though an amoeba shape is fine, too.
Roll out the dough.
Peel the dough off the counter and lay it in the skillet or on the griddle. Cook until the tortilla bubbles and puffs and the bottom browns in spots, 45 to 60 seconds. If any gigantic bubbles form, pierce them so the tortilla cooks evenly. Flip with a spatula and cook until the second side gets brown in spots and any translucent, raw-looking areas become opaque, another 45 to 60 seconds. (If the tortillas brown too quickly or start burning in spots, reduce the heat to medium low.) Transfer to a clean dishtowel and cover to keep warm. Repeat with the remaining dough, stacking and covering each tortilla as it’s cooked.
Cook the tortillas.
Because they're not loaded with preservatives, these tortillas taste best when freshly made. They'll stay pliable as long as kept warm. Leftover tortillas may be frozen (let cool thoroughly first.) Rewarm individual cooled or thawed torillas on a grittle or skillet, or wrap several tortillas in foil or heat in a 350ºF oven until warm and pliable, about 10 minutes.