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Boil water with diced tomato and salt. Cook the chicken breasts until tender. Save the stock – you'll use it twice. Shred into thick strips (not fine threads).
Oil + chopped garlic until lightly golden. Add the rice, stir, add the water (same volume as the rice), salt. Bring to a boil, lower to minimum, cover, 20 minutes. Don't lift the lid before then.
In a pot, oil + onion + garlic paste. Sauté for 45 minutes over low heat until the onion is completely cooked and sweet – this is the step most people rush, and that's why the ají comes out flat. Then add the ají amarillo and cumin to taste. Stir in at least 4 tablespoons of the chicken stock.
In another container, cubed French bread + evaporated milk + chicken stock. Blend with an immersion blender until smooth.
Mix the bread paste with the ají amarillo base in the pot. Lower the heat to minimum. Add the shredded chicken. Turn off the heat. Finish with Parmesan to taste and stir.
Rice + potato slices + ají de gallina on top. Garnish with hard-boiled egg and botija olives.