Season the chicken chunks generously with salt and pepper on all sides, making sure each piece is well coated with the seasoning.
Heat the olive oil in a large, heavy-bottomed pot or Dutch oven over medium-high heat, and brown the chicken pieces on all sides until they develop a beautiful golden color, about 8-10 minutes total, turning them carefully to ensure even browning.
Remove the golden chicken pieces from the pot and set aside on a plate, leaving the flavorful oil and browned bits in the pot.
In the same pot, add the minced garlic and diced onion, cooking over medium heat for 5-7 minutes until the onion is softened and lightly golden, scraping up any browned bits from the bottom of the pan.
While the onions cook, prepare the majado by placing the toasted bread, hard-boiled egg yolks, and ground walnuts in a mortar and pestle, grinding until you have a smooth paste. Add the flour and about ½ cup of warm chicken broth to this mixture, stirring until it forms a smooth, thick sauce with no lumps.
Return the majado mixture to the pot with the sautéed onions, stirring well to combine everything evenly and cooking for 2-3 minutes to let the flavors meld.
Add the remaining chicken broth along with the saffron threads, stirring to incorporate and bring the mixture to a gentle simmer.
Return the browned chicken pieces to the pot, reduce heat to low, and simmer covered for 20 minutes, stirring occasionally to prevent sticking, until the chicken is tender and the sauce has thickened to a velvety consistency. Taste and adjust seasoning with salt and pepper as needed, then serve immediately garnished with chopped hard-boiled egg whites.