Make the Creamy Chimichurri Sauce. Combine Greek yogurt, mayonnaise, minced shallot, finely chopped parsley, finely chopped cilantro, olive oil, red wine vinegar, pressed or grated garlic, and kosher salt in a small bowl. Whisk to thoroughly combine, then taste and season with more salt if needed. Set aside.
Season the Chicken. Combine garlic powder, kosher salt, and freshly cracked black pepper in a bowl and stir to evenly combine. Season the chicken breast all over with the seasoning, then set aside for about ten minutes at room temperature.
Cook the Chicken. Heat avocado oil in a pan over medium heat. Cook the seasoned chicken breast for about 4-5 minutes per side, until browned and the internal temperature reaches 165 F. Transfer the chicken to a bowl and cover with foil. Let it rest for at least five minutes, then shred it.
Cook the Jalapenos and Red Onions. In the same pan, add a couple of tablespoons of water to scrape the browned bits into the water, then add jalapenos and red onions. Cook for 3-4 minutes until softened and slightly crispy.
Mix in the Shredded Chicken. Transfer the shredded chicken and any liquids back to the hot pan.
Add Cilantro. Mix the chicken into the jalapenos and onions, then mix in the finely chopped cilantro. Turn off the heat.
Build the Tacos. Layer the shredded lettuce, sliced avocado, and shredded chicken into warmed flour tortillas. Top with crumbled feta cheese and drizzle with creamy chimichurri sauce. Serve warm!