Make the fried garlic Combine garlic and oil in a small saucepan. Cook over medium until bubbles form around garlic, about 1 minute; decrease heat to medium-low. Cook, stirring often, until garlic is light blond, 4 to 5 minutes. Remove pan from heat, and continue to stir. (Garlic will keep browning.) When garlic is golden brown, pour through a strainer set over a heatproof bowl. Let garlic cool on a paper towel; reserve garlic oil.
Make the salad Toss together cabbages, carrots, onion, sweet peppers, pickled and fresh ginger, and jalapeño in a large bowl. Add cilantro, fried chickpeas, peanuts, sesame seeds, and fried garlic; toss to combine.
Stir together pickled ginger brine, lime juice, fish sauce, and salt in a small bowl. Drizzle brine mixture over salad, adding reserved garlic oil to taste, if desired. Taste and add additional pickled ginger or pickled ginger brine, if desired. Serve immediately.