Add the 2 large skinless chicken breasts (approx. 230-300g) to a medium pot, then fill it with 1½- 2L water (6-8 cups) to fully cover the chicken breasts. Add the 1 medium carrot, 1 celery stalk, 1 medium onion, 1 garlic clove, and 1 tsp salt. Cover, then bring to a boil over high heat.
Reduce to medium heat to maintain a gentle simmer and cook for 20–25 minutes, or until the chicken is fully cooked and tender.
Remove the chicken from the pot and let it cool slightly before shredding. Strain the stock and reserve for the Aji de Gallina.
Place the 2 bread rolls (about 3-4 cups, cubed) in a bowl and pour 2¼ cups reserved chicken stock over it. Let it soak until the bread has absorbed the stock. Transfer the soaked bread and ½ cup walnuts to a blender alongside the 3-4 fresh aji amarillo peppers and blend for about 30–60 seconds, or until smooth and a loose paste forms. Set aside.
Heat ¼ cup vegetable oil in a frying pan over medium heat. Add ½ medium red onion and 2 garlic cloves and cook for about 3-5 minutes, stirring frequently, until softened and translucent without browning.
Stir in the jarred 1-1½ tbsp aji amarillo paste (aji mirasol)* and pinch of ground cumin then continue cooking over medium heat for about 2-3 minutes.
Add the bread/pepper liquid. Cook over medium heat for about 3-5 minutes, stirring constantly, until the mixture begins to thicken.
Stir in another ¼ cups reserved chicken stock and stir again, cooking for another 1-2 minutes.
Use an immersion blender to blend the sauce again so that it is completely smooth.
Stir in the shredded cooked chicken breast and ½ cup grated parmesan cheese. Season with salt and freshly ground black pepper. Pour in ½ cup evaporated milk and stir until smooth and well combined. Remove from the heat.
Meanwhile, cook 2 cups long grain white rice according to the package directions. Boil 4 medium yellow potatoes until fork-tender (about 15-20 minutes), then peel and cut into halves. Hard-boil the 2 eggs, then peel and halve them.
Arrange two potato halves on each serving plate. Spoon the Aji de Gallina over the potatoes and serve with the cooked white rice. Top each serving with half a hard-boiled egg, 4 black olives and fresh parsley sprigs.