To make the dressing, combine the oil, lime juice, vinegar, salt, and lemon pepper in a jar with a tight lid. Shake well to mix.
For the salad, in a large bowl, mix the cabbage and cilantro and toss with the dressing. Add in the rest of the ingredients (finely mince the 2 garlic cloves, and add those if you aren't using garlic paste) and toss lightly, or place these other vegetables around the salad platter as a garnish.
If you want, add some crumbled cojita or other Mexican white cheese for added flavor.