Preheat the oven to 375 degrees F. Toss the tortilla strips on a baking sheet with 1 tablespoon of oil, 1 teaspoon taco seasoning and 1/4 teaspoon salt. Spread out into an even layer and bake, stirring occasionally, until golden brown and crisp, about 20 minutes.
Heat the remaining 3 tablespoons oil in a small skillet over medium heat. Add the remaining 1 1/2 teaspoons taco seasoning and cook, stirring, until fragrant, about 1 minute. Remove from the heat and stir in the jalapeños, brine and 1/2 teaspoon salt.
Toss the beans, slaw mix, cilantro, Cheddar, tomatoes and onion with the taco-jalapeno dressing in a large serving bowl. Season with salt. Top with the tortilla strips and dollops of sour cream if using.
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