Rinse the chicken well under cold running water and pat dry with paper towels. Season generously with salt and pepper. In a large heavy skillet, heat the olive oil over medium/high heat. Brown the chicken pieces evenly on all sides, then transfer to a covered heatproof casserole. Add the onions and carrots to the hot skillet and cook, stirring occasionally, for about 10 minutes, until golden. Transfer them to the casserole with the chicken. Place the potatoes around the edges of the casserole and again season with salt and pepper. Add the bay leaf.
Pour off most of the fat from the skillet and, over high heat, deglaze it with the white wine. Cook, stirring and scraping the bottom and sides of the pan to release all the flavorful bits into the liquid, for about 3 minutes. Pour the wine over the chicken, add the stock and bring up to the boil. Reduce the heat to very low, cover and simmer for 25 to 30 minutes, until the chicken thighs test done. Check the pan occasionally to make sure the liquid is kept at a slow simmer. If it boils the chicken will be tough.
Transfer the chicken and vegetables to a platter with a slotted spoon and discard the bay leaf.
To make the picada: combine the almonds and garlic in a food processor and process them to a fine paste. Add the saffron and the hardboiled egg yolks only, process again and add enough of the liquid from the casserole to make a smooth paste. Return the casserole to mediumhigh heat and whisk the picada into the cooking liquid. Simmer until the sauce is reduced to about 3 cups, and taste for seasoning. Return the chicken and vegetables to the pan and turn to coat them with the sauce and heat through. Serve in the pan, sprinkled with the egg whites.