In a blender, combine fresh cilantro, jalapeños, mayonnaise, Cotija cheese, garlic, fresh lime juice, olive oil, salt, and black pepper. Blend the mixture until smooth yet chunky.

Slice the boneless skinless chicken breasts into thinner cutlets. In a bowl, toss the chicken with olive oil, cumin, paprika, garlic powder, salt, and black pepper. Heat a skillet over medium-high heat and sear the chicken for 5-7 minutes on each side until cooked through.

In a saucepan, combine rice, chicken broth (or water), butter, and salt. Bring to a boil, then reduce heat and simmer for 15-20 minutes.

Layer cilantro-lime rice in bowls, arrange sliced chicken on top, and drizzle with aji verde sauce.