In a large mixing bowl, whisk together the olive oil, minced garlic, soy sauce, lime juice, smoked paprika, ground cumin, oregano, salt, and pepper. Add the chicken thighs and toss until fully coated. Cover and refrigerate for at least 1 hour, or up to 6 hours for best flavor.

While the chicken marinates, in a blender, combine the jalapeños, cilantro, mayonnaise, cotija cheese, garlic cloves, and lime juice. Blend on high until smooth. With the blender running on low, slowly stream in the olive oil until creamy and emulsified. Season with salt to taste. Transfer to a jar and refrigerate until serving.

In a medium saucepan, heat the olive oil over medium heat. Add the finely chopped onion and cook until softened, about 3-4 minutes. Add minced garlic and cook for another minute until fragrant. Stir in the rinsed rice, coating it in the oil. Pour in chicken broth and salt, bring to a boil. Reduce heat to low, cover, and simmer for 15-20 minutes until liquid is absorbed. Remove from heat, let stand covered for 10 minutes, then fluff with a fork.

Heat a tablespoon of oil in a large skillet over medium-high heat. Cook the marinated chicken thighs for 6-8 minutes per side, or until internal temperature reaches 165°F (74°C) and juices run clear.

Let chicken rest for a few minutes, then slice. Serve over fluffy rice, drizzled generously with green sauce.