To make the vin cotto: Combine all the ingredients in heavy-bottomed saucepan. Bring to a boil over high heat and then simmer, stirring occasionally to ensure that the honey does not burn, until the wine is reduced to 1/4 of its original amount, about 20 minutes. Remove from the heat and let cool. Remove the cinnamon sticks before using.
To make the chicken: Remove the giblets, clean and pat dry the chicken. Cut the chicken into 8 pieces, leaving the bones intact. In a 12 to 14-inch saucepan, heat 2 tablespoons olive oil until hot but not smoking. Add the chicken pieces, skin side down, and brown on both sides over high heat, about 4 minutes per side, season with salt. When the chicken is brown, add onion and carrot, caramelize and toss. . Add the olives, raisins, capers, pine nuts, and almonds, deglaze with 1/2 vin cotto, reducing by 1/2.
Add the remaining 1/2 cup vin cotto and turn the heat to high, so that the wine comes to a boil. In a small bowl, combine the vinegar and the sugar. Add to the pan and cook over high heat until all the wine and vinegar has evaporated. Season, to taste, with salt and pepper and serve hot, garnished with chili flakes, parsley, extra-virgin olive oil and cracked black pepper.