Combine cilantro, jalapeño, mayonnaise, Cotija cheese or Parmesan, garlic, lime juice, olive oil, salt, and black pepper in a blender; blend until smooth to make Aji Verde.

Season the chicken breasts with ground cumin, paprika, garlic powder, and salt.

Heat olive oil in a skillet over medium-high heat; sear the chicken breasts until golden brown and cooked through.

In a saucepan, combine rice and water or chicken broth; bring to a boil, then cover and simmer until rice is cooked.

Stir butter or olive oil, salt, cilantro, and lime juice into the cooked rice.