Just before serving, heat each one for a few seconds per side on the same griddle (again, very hot). I actually use a grate over an open flame - same thing, a few seconds per side. As they heat, you can often see the tortillas visibly soften and puff up (they'll flatten again as soon as they cool). As soon as you take each one off the heat, stack them and cover with a cotton dishtowel, cloth napkin, or paper towels. They'll stay soft and warm long enough to get them to the table. For a slightly longer holding time, you can roll and wrap a few at a time in foil.
In homes where tortillas are served with every meal, you'll often find a covered ceramic dish designed for the purpose of keeping them warm. There are also Styrofoam versions of these warmers - they look tacky but they really work well.
One question to add - what's the best way to reheat the tortillas, or at least keep them pliable, if I wanted to make them a couple of hours in advance? Thanks!
Great anecdote about the state of Texas, latoscana! My students made fresh tortillas last week, and some of the shapes were of the creative variety: states, animals, clouds, but ultimately all wonderful in texture. Once you've made really good ones, regardless of the perfect shape, why would anyone go back?
A comal is a large, shallow ceramic plate that sits directly on a fire. Perfect for roasting veggies, in addition to cooking tortillas. For those without a comal over a live fire, any heavy griddle or cast iron skillet over high heat works fine - and that's just what the abuelas use. Cook one at a time. They puff up during cooking but there is no need to weight it - just flip it to do both sides. They cook very quickly (should only be 1/8 inch thick at most). As sarah k says, keep the finished tortillas covered with a dish towel to keep them warm and soft.
The first time I made them, my father-in-law held one up and asked "Is this supposed to be the state of Texas?" It wasn't very circular. Tasted fine.
Yikes! I wouldn't try it on a panini press, but like the others have said, a nice, smooth skillet works well. I use a 9 inch cast iron skillet, dry, not oiled. Make sure it's hot. It should take about 30 seconds per side. I actually heat up two skillets, throw one tortilla in the first, prepare the second, toss the first tortilla into the second skillet, the second tortilla into the first skillet... like an assembly line. There's just enough time to roll out a new piece of dough (between the sides of a heavy duty ziploc bag that I just cut all the sides off of, so it opens like a book). When the second side is cooking, I use a kitchen towel to gently push down on the tortilla. When the tortilla pushes back, it's done! It will puff up like a balloon. Then I have a plate ready with a thick towel, throw the finished tortilla one, wrap it, flip the next one, etc. If you stack them while each one is hot, and make sure to re-wrap the stack each time, they will steam lightly, and be nice and pliable when you're ready to use them. It takes less than 10 minutes to make 16-20 tortillas this way.
I agree with boulangere. A cast iron skillet would be better. But look for some kind of weight that you can put on top. A brick, a flowerpot, a smaller cast iron. Some "panini" griddles have reversable grill sheets, one side with ridges and one without. The latter might work.
The ridges of a panini press might do funny things to the tortillas as you cook them. I would just use a heavy frying pan (preferably case iron) or griddle, since a comal is basically just a griddle.
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In homes where tortillas are served with every meal, you'll often find a covered ceramic dish designed for the purpose of keeping them warm. There are also Styrofoam versions of these warmers - they look tacky but they really work well.
The first time I made them, my father-in-law held one up and asked "Is this supposed to be the state of Texas?" It wasn't very circular. Tasted fine.