Preheat oven to 400°F. Season the chicken liberally on both sides with salt, pepper and paprika. Allow to sit for about 10 minutes at room temperature.
Set a very large skillet or dutch oven over medium-high heat. Once hot, add 2 tablespoons oil and then add in half of the chicken. Cook until browned on both sides, a few minutes per side. Transfer to a plate or platter and set aside. Continue to brown the remaining chicken.
Once the chicken has browned, drizzle in the remaining tablespoon of oil into the hot skillet. Add in the onion, aji peppers, and garlic and cook until softened, about 5 minutes. Stir in the tomatoes and cook for about a minute longer. In a small measuring cup or bowl, whisk together the soy sauce, vinegar, and beef stock. Then pour into the skillet with the vegetables. Deglaze the pan with the sauce and use a wooden spoon to scrape up the bits at the bottom of the pan. Bring to a simmer and then lay in the chicken (along with any accumulated juices) in a single layer. Carefully transfer to the oven and cook until the chicken reaches an internal temperature 165°F, about 35 to 40 minutes.
In the meantime, spread the fries on a baking sheet and cook until crispy, according to the package directions. Try to time it so that they're done around the same time when the chicken is done. Once both are finished, transfer the fries to the chicken and give it all a gentle stir. Top with the fresh cilantro. Serve with cooked white rice on the side and the aji verde sauce (recipe follows). Enjoy!
To make the aji verde sauce: combine all of the ingredients in a blender and blend on high until smooth and creamy. You might have to stop the machine and use a spoon to help it along a few times. Once blended, give it a taste and adjust seasoning accordingly, adding more salt as needed. Transfer to an airtight container and keep in the fridge for up to a week.