The dough is very simple: flour, a little shortening, a little baking powder, some salt. The result is soft and pliable. You want to roll them out to about 1/4" thickness---not too thin.
It turns out that the secret to making them puff is to spoon hot grease on the top while they are cooking. About a minute per side is all it takes.
Sopapillas cry out for something to fill that puffy interior. These days, New Mexicans will stuff them with anything: chili, cheese, ... I prefer the traditional honey. The technique is to poke a hole in the top and drizzle it in. Be sure to turn the sopapilla a little to touch every nook with honey.
I paired the sopapillas with homemade chili: pork confit, red beans, chicken stock, and some Patak bacon for good measure.