Place the sweetbreads in a bowl and cover them with fresh water. Let them rest for 5 minutes and then drain.
Precook the sweetbreads in a saucepan or pot (I used my large skillet) with water, the ¼ onion, garlic cloves, and bay leaf over medium heat (use enough water to cover the sweetbreads). Bring to a boil and then reduce the heat to simmer for about 15 minutes, until the skin of the sweetbreads looks firm and it has changed color from pink to a pale beige.
Remove from the saucepan and reserve some of the cooking liquid. Allow the sweetbread to cool enough for you to handle it and remove the outer membrane.
If some of the pieces of the sweetbreads are too thick, cut them in half by slicing them lengthwise**, then proceed to chop them into small bite-size pieces.
Heat the oil in a large skillet or comal; we are going to slightly brown the sweetbreads and also warm the tortillas in the same skillet. Once the oil is hot, add the chopped sweetbreads and stir-fry them until the outer skin is golden (you have to stir them frequently). Add more salt if needed.
In the same skillet, warm the tortillas, adding a couple of tablespoons of the cooking broth on them. This will soften the tortillas and also infuse some flavor into them (just like it’s done in many taquerias). Do not leave the tortillas on the skillet for longer than is needed to warm them, because if you leave them there for too long, they can start to break (your experience will vary depending on the type and brand of tortilla you use).
To serve, divide the meat among the tortillas, then top them with the chopped onion and cilantro and your favorite salsa. Serve with some lime wedges, for those that like to add a few drops of lime to their tacos. If using the small taqueria-style tortillas, use 2 tortillas per taco.