Season chicken with cumin, paprika, turmeric, salt, and pepper in a bowl.
Heat olive oil in a large skillet over medium heat, cook chicken until browned and cooked through, then remove and set aside.
In the same skillet, sauté onion, garlic, and red bell pepper for 3-4 minutes until softened.
Add rice to the skillet and stir for 1 minute to coat with oil and spices.
Pour in chicken broth, stir, bring to a boil, reduce heat to low, cover, and simmer for 15 minutes.
Stir in frozen peas and return cooked chicken to the skillet, cover, and cook for another 5 minutes until rice is fluffy and peas are tender.
Add chopped cilantro and lime juice, fluff the rice with a fork, and adjust seasoning if needed.
To prepare the green sauce, combine cilantro leaves, mayonnaise, jalapeño, garlic, lime juice, olive oil, Parmesan cheese, salt, and pepper in a blender and blend until smooth. Adjust seasoning to taste.
Serve the chicken and rice in bowls, drizzle with green sauce, and garnish with fresh cilantro and lime wedges.