Add cilantro, jalapeños, mayonnaise, Cotija cheese, garlic, lime juice, olive oil, salt, and pepper to a blender or food processor. Blend for 20-30 seconds until mostly smooth but still showing green flecks. Taste and adjust salt or lime juice as needed. Transfer to a bowl and refrigerate while preparing the rest of the meal.

In a medium saucepan, combine rice, water or broth, butter, and salt. Bring to a boil over medium-high heat, then immediately reduce heat to low, cover tightly, and simmer for 15 minutes. Remove from heat and let stand covered for 10 minutes. Fluff with a fork and fold in chopped cilantro and lime juice right before serving.

While rice simmers, prepare chicken. If chicken breasts are thick, slice them horizontally to create thinner cutlets about ½ inch thick. In a large bowl, toss chicken with olive oil, cumin, paprika, garlic powder, salt, and pepper until evenly coated.

Heat a grill pan or large skillet over medium-high heat until very hot. Working in batches to avoid crowding, sear chicken for 5-7 minutes per side until deeply charred and internal temperature reaches 165°F. Let rest for 5 minutes before slicing into thick pieces.

Spoon cilantro-lime rice into bowls, top with sliced chicken, and drizzle generously with aji verde. Garnish with extra cilantro if desired and serve immediately.