To a medium pot, add 3¼ cups of the nopales, the garlic cloves, onion, and enough cold water to cover by 2 inches. Bring to a boil over medium heat and cook until the nopales turn light green, about 10 minutes, then drain, discarding the cooking liquid. (This first round of cooking removes the goo from the nopales.) Return the nopales to the pot, and add 2 teaspoons salt and enough cold water to cover by 2 inches. Bring to a boil over medium heat, then lower the heat to medium-low to maintain a strong simmer, and cook until the nopales are tender when poked with the tip of a knife, 18– 22 minutes. Drain, once again discarding the cooking liquid. Remove and discard the garlic, and set the nopales aside.
To a medium bowl, add the remaining ¾ cup raw nopales and 1 tablespoon plus 1½ teaspoons salt, and toss well to combine. Set aside at room temperature until the nopales have softened and released their slime, about 20 minutes. Rinse and drain well, then set aside.
To a large skillet over medium heat, add the olive oil. When the oil is hot, add the minced garlic, guajillo chile, chile de arból, reserved boiled nopales, oregano, and cumin, and cook, stirring frequently, until fragrant, about 5 minutes. Stir in the vinegar, cook for 1 minute more, then remove the skillet from the heat. Add the reserved raw, salted nopales and toss well to combine; season to taste with black pepper and additional salt, then transfer to a large bowl and serve at room temperature.