In a large bowl, combine olive oil, cumin, smoked paprika, garlic powder, oregano, salt, black pepper, and lime juice. Add chicken thighs and coat thoroughly. Cover and refrigerate for at least 30 minutes or up to overnight.

In a blender or food processor, combine cilantro, jalapeños, garlic, mayonnaise, lime juice, olive oil, and Parmesan cheese if using. Blend until smooth and creamy. Add water one tablespoon at a time if sauce is too thick. Season with salt to taste and refrigerate.

Heat olive oil or butter in a medium saucepan over medium heat. Add diced onion and cook until softened, about 3-4 minutes. Add minced garlic and cook for another minute.

Add rice to the pan and stir to coat with oil and aromatics. Cook for 2 minutes, stirring occasionally, to lightly toast the rice.

Stir in ground turmeric until rice is evenly coated. Pour in chicken broth or water and add salt. Stir once, bring to a boil, then reduce heat to low, cover tightly, and simmer for 15-18 minutes without lifting the lid.

Preheat grill or grill pan to medium-high heat. Remove chicken from marinade and place on grill skin-side down. Cook for 6-7 minutes until skin is crispy and charred. Flip and cook another 6-7 minutes until internal temperature reaches 165°F.

Transfer grilled chicken to a plate and let rest for 5 minutes.

Remove rice from heat and let stand covered for 5 minutes. Fluff with a fork and stir in fresh cilantro if desired.

Divide turmeric rice among serving bowls. Top with grilled chicken thighs. Drizzle generously with aji verde sauce and garnish with extra cilantro leaves and lime wedges.