Drain the potatoes in a colander and set aside.
Heat a heavy-bottomed skillet over medium-high heat. Add the vegetable oil and diced onion, cooking until the onion's softened, about 3 minutes.
Add the chorizo and cook, breaking it up into smaller pieces, until it browns and crisps, 5 to 7 minutes.
Add the potatoes to the skillet, gently folding them into the chorizo. Cook until warmed through, 3 to 5 minutes.
Remove the filling from the heat and cover to keep it warm while you shape and cook the gorditas. To make ahead, cool to room temperature and refrigerate, covered, until ready to reheat and serve (up to five days later).
To make the dough: Weigh your masa harina; or measure it by gently spooning it into a cup, then sweeping off any excess. In a large, shallow mixing bowl, combine the masa harina and salt. Gradually add the warm water, stirring with your hands to make a cohesive dough.
Using your hands, mix and knead the dough in the bowl for a minute or so, until it’s smooth and somewhat firm; it should feel like Play-Doh. If the dough sticks to your hands and feels wet, add more masa harina a teaspoon to a tablespoon at a time. If you roll a piece into a ball and squeeze it and the edges crack, add more water a teaspoon to a tablespoon at a time.
Preheat a comal, a cast iron or nonstick pan, or a griddle over medium heat for 5 minutes, or until evenly hot.
To shape the gorditas: Cut two round or square pieces of food-safe plastic — from a plastic produce or zip-top bag — to a size about 1/2" larger than the diameter of your tortilla press. Set aside.
Divide the dough into 10 pieces (about 60g to 65g each) and roll each piece into a ball. Place on a clean work surface and cover them with plastic or a damp kitchen towel to keep them soft.
Working with one ball of dough at a time, sandwich it between two pieces of plastic. Place the plastic-enclosed dough on the bottom plate of a tortilla press; if you don't have a tortilla press see "tips," below. Gently press the dough until it’s a scant 1/4” thick and about 4 1/2” in diameter; you may need to press it a couple of times to get the desired thickness.
To cook the gorditas: Peel the top piece of plastic and then the bottom piece away from the gordita. Quickly but gently lay the gordita on the hot pan.
Cook the gordita on both sides until crispy and speckled with light brown spots, 1 to 2 minutes per side.
Flip the gordita back to its original side and cook it until it puffs, 10 to 15 seconds. If the gordita doesn’t puff on its own, use your finger (or a spatula) to gently poke it a few times near the center; this will encourage it to separate into layers and puff. Once it puffs, let the gordita cook for 15 to 20 seconds longer.
Remove the gordita from the heat and wrap it in a clean kitchen towel.
Repeat with the remaining pieces of dough.
When the gorditas are cool enough to handle cut a slit along the outer edge of each with a paring knife, sliding the knife between the two sides where the air pocket has formed. You want to cut about halfway around the gordita, leaving the other half intact to create a pocket.
Stuff each gordita with about 1/4 cup of the filling, add your desired toppings, and serve.
Storage instructions: Unfilled gorditas can be wrapped in a kitchen towel and stored at room temperature for up to one day. Refrigerate leftover filled gorditas, wrapped in a kitchen towel and sealed in a plastic bag, for two to three days, or freeze for two to three months.
