Combine lime juice, 1 tablespoon olive oil, 2 minced garlic cloves, salt, cayenne pepper, ground cumin, and black pepper in a large zip-top bag or bowl. Pat the chicken thighs dry with paper towels—this ensures better flavor absorption and helps them cook evenly. Add the chicken to the marinade, seal or cover, and mix well to coat all pieces. Refrigerate for at least 30 minutes, though longer (up to 4 hours) will deepen the flavor even more.
While the chicken marinates, make the slaw so flavors can meld together. In a small bowl, whisk together mayonnaise, sour cream, 3 tablespoons fresh lime juice, 1 minced garlic clove, chopped cilantro, kosher salt, and black pepper until smooth. In a large bowl, toss the shredded cabbage with the dressing until evenly coated. Set aside at room temperature—I find this actually tastes better than chilled slaw because the flavors are more vibrant.
Preheat your oven to 400°F. Coat a baking dish (9x13 inch or similar) with the remaining 1 tablespoon of olive oil. Remove the marinated chicken from the refrigerator and arrange it in a single layer in the prepared dish, skin-side up if available. Sprinkle lightly with salt and pepper. Roast for 30-40 minutes, basting the chicken with pan juices halfway through cooking. The chicken is done when it reaches an internal temperature of 165°F and the skin is golden and slightly crispy.
Remove the baking dish from the oven and carefully pour the pan juices into a small bowl—these flavorful drippings are liquid gold for your tacos. Let the chicken rest for 10 minutes on the baking sheet (this keeps the meat juicy and easier to shred). Once cooled slightly, use two forks to shred the chicken into bite-sized pieces directly in the baking dish. Pour the reserved pan juices back over the shredded chicken and toss to combine, ensuring every piece is coated with that savory, lemony flavor.
Warm your tortillas in a dry skillet over medium heat for about 30 seconds per side, or wrap them in foil and warm in the oven. Arrange the warm tortillas on a serving platter. Set out the shredded chicken, cabbage slaw from Step 2, crumbly cheese, hot sauce, and fresh avocado slices in separate bowls so guests can build their own tacos. Let each person layer their tortilla with chicken, slaw, cheese, avocado, cilantro, and hot sauce to taste.