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For the sopes: Combine the masa harina, flour, baking powder and salt in a mixing bowl. Make a well in the center and slowly add the warm water while incorporating the dry ingredients using a stiff spatula. Once the dough comes together, transfer it to a floured surface and knead it by hand until it is smooth and not crumbly, about 5 minutes.
Roll the dough to 1/4-inch thickness and then cut it into 2-inch circles with a biscuit cutter or the rim of a glass; you should get 36 circles. Re-roll and re-cut scraps of dough until all of it is used. Create a ridge around the edge of each sope using your thumb, and working from the center outwards. You are trying to make a small well for the toppings to rest in once the dough is fried.
Fill a cast-iron skillet with 1 1/2 inches of vegetable oil and heat to 350 degrees F over medium-high heat. Once the oil is hot, fry the sopes until their edges are crispy and just starting to brown, about 3 minutes. Flip and cook for another 3 minutes. Transfer the sopes to a paper-towel-lined plate and season with salt as they come out of the oil.