In a high-speed blender, combine fresh cilantro, diced jalapeños, mayonnaise, Cotija or Parmesan cheese, minced garlic, fresh lime juice, olive oil, fine salt, and black pepper. Blend until mostly smooth, about 30-60 seconds. Transfer to a bowl, cover, and refrigerate.

Slice the boneless, skinless chicken breasts into thin cutlets. Coat with olive oil, cumin, paprika, garlic powder, salt, and pepper. Heat a grill pan over medium-high heat and sear chicken for 5-7 minutes on each side, until charred and cooked through. Let rest before slicing.

In a saucepan, combine long-grain white rice, water or low-sodium chicken broth, butter or olive oil, and salt. Bring to boil over medium-high heat, then reduce heat to low, cover, and simmer for 15-20 minutes until rice is tender. Fluff with a fork and stir in cilantro and lime juice.

To serve, spoon cilantro-lime rice into bowls, top with sliced chicken, drizzle with Aji Verde, and garnish with cilantro leaves.