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In the work bowl of a food processor, pulse together the flour, salt, and baking powder.
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Add the shortening and pulse until the mixture resembles a coarse meal.
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Stir in 2/3 cup warm water, and pulse until a shaggy dough forms.
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Turn the dough out onto a floured surface and knead until smooth and soft, 3 to 4 minutes. After kneading, the dough shouldn't be very sticky.
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Portion the dough into 8 equal pieces, and shape each piece into a ball. Cover the dough and let rest on the counter for at least 30 minutes, up to 2 hours.
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When ready to cook, heat a large (11-12 inch), dry skillet or griddle over medium heat until hot.
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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 - 10 inch round. The dough should be so thin that you can vaguely see the pattern of your countertop through it, and more or less circular.
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Peel the dough off the counter and lay it in the skillet. Cook until the tortilla bubbles and puffs, and the bottom browns in spots, 45 - 60 seconds. If any gigantic bubbles form, pierce them so the tortilla cooks evenly.
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Flip with a spatula, and cook until the second side gets brown in spots, and nay translucent, raw-looking areas become opaque, another 45 to 60 seconds. Transfer to a clean dish towel.
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Repeat with the remaining dough.