Whisk together the yogurt, lime juice, tequila, garlic, garlic powder, onion powder, paprika, salt, cumin, cinnamon, cloves, and pepper in a large bowl. Add the chicken thighs and toss until thoroughly coated.
Heat a large non-stick skillet over medium-high heat. Sear the chicken for 1 to 2 minutes per side, then reduce the heat and cook for 2 to 5 minutes per side until the internal temperature reaches 165°F. Use a small amount of the marinade for cooking, but do not add all of it to the pan. Transfer the chicken to a cutting board and let it rest for 5 minutes before slicing.
Combine the Garlic White Sauce ingredients in a small bowl and whisk until smooth. Adjust the seasoning with additional salt, cumin, or garlic as desired.
Distribute the cooked rice among four bowls. Top with the sliced chicken, pickled onions, cucumber, feta, tomatoes, and avocado. Drizzle with the Garlic White Sauce and garnish with lemon wedges, parsley, and mint.