In a blender, combine fresh cilantro, jalapeños, mayonnaise, Cotija cheese, garlic, fresh lime juice, olive oil, fine salt, and black pepper. Blend until mostly smooth but slightly chunky.

Transfer the aji verde to a bowl, cover, and refrigerate while preparing the meal.

Slice thick chicken breasts into cutlets, toss with olive oil, cumin, paprika, garlic powder, salt, and pepper until well-coated, and let sit for about 10 minutes.

Heat a grill pan over medium-high heat, add the chicken, and sear for 5-7 minutes on each side until cooked through.

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

After cooking, let the rice rest for 5 minutes, then fluff with a fork and mix in cilantro and lime juice.

To assemble, place cilantro lime rice at the base, top with chicken slices, and drizzle with aji verde. Garnish with extra cilantro and lime wedges.