Wash and dry all produce. Zest one of the limes, then cut all limes in half. Squeeze juice from six halves into a medium bowl (we’ll use the last two later). Thinly slice jalapeño into rounds, removing ribs and seeds first for less heat.

Whisk a drizzle of olive oil, half the lime zest, 11/2 tsp sugar, and a big pinch of salt and pepper into bowl with lime juice. Add cabbage and half the jalapeño (use more for extra heat). Toss to combine. Set aside to marinate.

Cut each apple into eight wedges; trim and discard core and seeds. Thinly slice wedges crosswise until you have 2 cups sliced apple (save the rest for another use). Trim, then thinly slice scallions. Add apple and scallions to bowl with cabbage slaw. Toss to combine. Season with salt.

Pat chicken dry with a paper towel. Heat a large drizzle of olive oil in a large pan over medium-high heat (we used nonstick). Add chicken, Southwest spice, and a big pinch of salt and pepper. Cook, tossing occasionally, until chicken starts to brown, 3-5 minutes. Pour in 1/4 cup water, scraping bottom of pan to release browned bits. Cook until chicken is coated in a loose sauce, about 1 minute more. Remove from heat.

Meanwhile, stir together sour cream, remaining lime zest, and juice from one lime half in a small bowl. Add water, 1 tsp at a time, until mixture has a drizzling consistency. Season with salt.

Wrap tortillas in a damp paper towel and microwave until warm, about 30 seconds. Roughly chop cilantro. Divide tortillas between plates. Divide chicken between tortillas, then top with slaw, crema, and cilantro. Garnish with jalapeño to taste. Cut remaining lime into wedges and serve on the side.