In a blender, combine fresh cilantro, chopped jalapeños, mayonnaise, crumbled Cotija cheese, garlic cloves, fresh lime juice, olive oil, fine salt, and black pepper. Blend on high until mostly smooth, about 1-2 minutes. Transfer to a bowl and refrigerate for at least 15 minutes.

Slice the boneless, skinless chicken breasts into thin cutlets. In a mixing bowl, toss with olive oil, ground cumin, smoked paprika, garlic powder, salt, and pepper until coated. Heat a grill pan over medium-high heat and sear for 5–7 minutes per side until cooked through.

In a saucepan, combine long-grain white rice with water, butter or olive oil, and fine salt. Bring to a boil, then reduce heat to low, cover, and simmer for 15-20 minutes. Let it rest for 10 minutes before fluffing with a fork.

Mix freshly chopped cilantro and lime juice into the rice. Serve a scoop of rice in each bowl topped with sliced chicken and a drizzle of aji verde sauce. Garnish with cilantro.