Place the beef sweetbreads in a large bowl and cover completely with cold water. Let them soak for at least 1 hour to remove impurities, then drain. If the water looks very cloudy, I like to repeat this step once more.

Transfer the soaked sweetbreads to a medium pot and cover with fresh cold water. Add the salt and vinegar. Bring to a gentle boil, then reduce heat and simmer for about 10 minutes, until the sweetbreads turn pale and feel slightly firm.

Drain the sweetbreads and immediately place them in a bowl of cold water to stop the cooking. Once cool enough to handle, gently remove the outer membrane and trim off any tough or gristly bits.

Cut the cleaned sweetbreads into bite-size pieces. If some pieces are thick, slice them lengthwise first so they cook evenly.

Heat oil or butter in a large skillet over medium-low heat. Add the sweetbreads in a single layer and cook slowly, turning occasionally, until golden and crisp on the outside, about 10–15 minutes. Season with additional salt to taste.

Warm the corn tortillas in a dry skillet or directly over a flame until soft and pliable.

Assemble the tacos by dividing the cooked sweetbreads among the tortillas. Top with chopped onion, cilantro, salsa if using, and a squeeze of fresh lime. Serve immediately.