Add garlic, soy sauce, lime juice, olive oil, cumin, paprika, oregano, and black pepper to a blender. Blend on high for 30-45 seconds until completely smooth with no garlic chunks visible.

Place the chicken thighs in a large zip-top bag and pour the marinade over them. Seal the bag and massage gently to ensure all pieces are coated. Refrigerate for 12 hours (or between 8 to 24 hours), flipping the bag halfway through for even marinating.

To make the green sauce, combine jalapeños, cilantro, green onions, garlic, mayonnaise, Greek yogurt, lime juice, salt, and black pepper in a clean blender. Blend until smooth, about 45 seconds. With the motor running on low, slowly drizzle in olive oil through the top opening. Transfer to a bowl, cover, and refrigerate.

Preheat your grill to medium-high heat (around 350°F). Remove the chicken from the marinade and shake off excess liquid until glossy but not dripping. Place the chicken on the grill grates and close the lid. Cook for 5-6 minutes without moving it.

Flip the chicken thighs using tongs and cook another 5-6 minutes with the lid closed. Use a digital thermometer to verify that the internal temperature reaches 165°F. Let the chicken rest for 3-4 minutes before serving with the green sauce.

Alternative oven method: Preheat your oven to 500°F. Place the chicken in a 13x9-inch roasting pan with 1 cup water. Bake uncovered for 30 minutes, then tent with foil and cook for an additional 15 minutes until the internal temperature reaches 165°F.