In a blender, combine fresh cilantro, jalapeños, mayonnaise, Cotija cheese, garlic, lime juice, olive oil, salt, and pepper. Blend until mostly smooth, about 30-60 seconds, then refrigerate the sauce while preparing the chicken and rice.

If chicken breasts are thick, slice them into thinner cutlets. Coat with olive oil, then season with cumin, paprika, garlic powder, salt, and pepper. Heat a grill pan or skillet over medium-high heat and sear chicken for 5-7 minutes per side until cooked through.

In a saucepan, combine rice, water or broth, butter, and salt; bring to a boil. Reduce heat, cover, and simmer for 15-20 minutes until liquid is absorbed. Let it sit covered for another 5 minutes, then fluff with a fork and fold in cilantro and lime juice.

To serve, place cilantro-lime rice on each plate, layer sliced chicken, and drizzle with Aji Verde sauce. Garnish with additional cilantro and serve lime wedges on the side.