For the chicken: Place an oven rack in the center of the oven. Preheat the oven to 400 degrees F. Spray a heavy baking sheet with vegetable oil cooking spray.
Rub the chicken on all sides with the oil and season with salt and pepper. Arrange the chicken pieces in a single layer on the prepared baking sheet. Bake until a meat thermometer inserted into the thickest part of each piece of chicken registers 160 degrees F, 35 to 45 minutes. Let the chicken rest for 15 minutes.
For the sauce: Place the bread and half-and-half in the bowl of a food processor. Allow the bread to soak up the liquid, about 10 minutes.
In a 10-inch nonstick skillet heat the oil over medium-low heat. Add the shallots and cook, stirring occasionally, until soft, 3 to 4 minutes. Add the garlic and cook until aromatic, about 30 seconds. Cool slightly and add to the food processor with the soaked bread. Add the broth, cheeses, 1/2 cup walnuts, Aji Amarillo paste, and turmeric. Blend until smooth. Pour the sauce back into the skillet and bring to a simmer over medium heat. Simmer until slightly thickened, about 5 minutes. Season with salt.
Spoon some of the sauce on a platter and arrange the chicken on top. Sprinkle with the remaining toasted walnuts and cilantro (or parsley, if using) and serve.
Cook's Note: To toast the walnuts, arrange in a single layer on a baking sheet. Bake in a preheated 350 degrees F oven for 6 to 8 minutes until lightly toasted. Cool completely before using.
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