Start by whisking Greek yogurt, mayonnaise, minced shallot, parsley, cilantro, olive oil, red wine vinegar, garlic, and salt together. Taste and adjust seasoning. Set aside in the fridge while you prepare the chicken.
Heat avocado oil in a skillet, then cook chicken breasts until fully cooked, about 5–7 minutes per side. Sprinkle with garlic powder, salt, and pepper while cooking for maximum flavor.
Remove chicken from skillet and shred with two forks. Return to the pan, toss with red onion, jalapeño, and chopped cilantro, and cook for another 2–3 minutes.
Warm tortillas, then layer shredded chicken, lettuce, avocado slices, and crumbled feta. Drizzle generously with creamy chimichurri sauce. Serve immediately while warm.