Add the chicken thighs and A Dozen Cousins Peruvian Pollo a la Brasa Marinade to a bowl or zip-lock bag and toss until every piece is completely and evenly coated.

Heat the neutral oil in a large skillet over medium-high heat. Remove the chicken from the marinade and sear for 5–6 minutes per side until deeply caramelized and cooked through to 165°F internally. Let rest 5 minutes, then shred into generous pieces using two forks. Set aside.

Make the aji verde. Add the cilantro, jalapeños, aji amarillo paste, garlic, mayo, sour cream, lime juice, queso duro or feta, white vinegar, and salt to a blender and blend on high until completely smooth and vivid green. Stream in the neutral oil while blending until fully emulsified and silky. Add cold water one tablespoon at a time until you reach a creamy, pourable consistency. Taste and adjust salt and lime. Refrigerate until ready to serve.

Make the cheese sauce. Pour the evaporated milk into a small saucepan over medium-low heat and warm until steaming but not boiling — never let it boil or the sauce will break. Whisk in the cornstarch slurry and stir for 1 minute until slightly thickened. Reduce the heat to the lowest setting and add the torn American cheese pieces a few at a time, whisking constantly until each addition is completely melted before adding the next.

Once all the American cheese is fully incorporated, add 1½ cups of the freshly grated cheddar in small handfuls, whisking constantly until completely smooth and glossy. Add the garlic powder, smoked paprika, and salt and stir to combine. Taste and adjust seasoning. The sauce should be completely smooth, deeply cheesy, and pourable — if it feels too thick, add a splash of warm evaporated milk and whisk until loosened. Keep on the lowest heat setting possible, stirring occasionally, until ready to use.

Preheat the oven to 400°F. Spread half the tortilla chips in an even layer in a large oven-safe skillet, cast iron, or baking dish. Drizzle half the cheese sauce generously over the first chip layer, then scatter half the black beans, half the shredded chicken, and ½ cup of the remaining shredded cheddar cheese. Add the remaining chips in a second layer and drizzle the remaining cheese sauce generously over the top. Scatter the remaining black beans, chicken, and shredded cheddar.

Bake for 12–15 minutes until everything is hot and bubbling.

Remove from the oven and immediately top with thinly sliced red onion and fresh cilantro. Drizzle the aji verde generously back and forth over the entire surface. Add a generous dusting of ground cotija and serve immediately.