Whisk the flour, salt, and baking powder together in a mixing bowl. Mix in the shortening with your fingers until the flour resembles cornmeal. Add the water and mix until the dough comes together; place on a lightly floured surface and knead a few minutes until smooth and elastic. Cover with saran wrap and rest dough for 30 minutes.
Divide the dough into approximately 8 equally sized pieces for large tortillas, make each piece into a ball. Lightly flour your surface and rolling pin to roll each dough ball into a thin, round tortilla. Roll out from the center of each dough ball, picking up and turning 90 degrees every time you roll to get a round tortilla. It will almost feel like you are rolling out pizza dough.
Preheat a large skillet over medium-high heat.
Place tortilla in a dry, hot skillet (we like hot cast iron skillets) for 5 seconds on the first side and 5 seconds on the second size. The tortillas will become slightly bubbly and turn a slight golden/brown.
Once cooked, stack and wrap tortillas in a damp towel or toweled tortilla warmer so they will not become crunchy while you finish cooking the remaining tortillas. The tortillas will come out soft and beautiful.