How to Make It
In a small skillet, toast the allspice, peppercorns, cumin seeds, cinnamon and cloves over moderately high heat until fragrant. Transfer to a spice grinder and let cool completely. Grind to a powder and transfer to a small bowl. Stir in the paprika, chipotle and ancho powders, salt and sugar.
On a large rimmed baking sheet, flatten the chicken by pressing on the breastbone. Sprinkle the chicken all over with the Adobo Rub. Cover and refrigerate for at least 30 minutes or up to 2 hours. Bring the chicken to room temperature before grilling.
In a glass measuring cup, cover the guajillo chiles with the boiling water. Cover and let stand until softened, about 15 minutes.
In a medium saucepan, combine the orange zest and juice with the vinegar, corn syrup, brown sugar, honey, chopped mango, ginger, habanero and coriander. Add the guajillos and their soaking liquid and bring to a boil. Boil over moderately high heat until reduced by half, about 7 minutes. Transfer the sauce to a blender and puree. Scrape the puree back into the saucepan and simmer over moderate heat until reduced to 1 1/2 cups, about 15 minutes. Season with salt.
Light a grill. Oil the grill grate and put the chicken on it, skin side down. Grill over moderately high heat until charred, about 7 minutes. Turn the chicken and cook until charred on the other side, about 5 minutes. Turn the heat off in half of the grill or rake the coals to one side, away from the chicken. Cover and grill the chicken over indirect heat, turning halfway through, until an instant-read thermometer inserted in the inner thigh registers 160°, about 1 hour.
Brush half of the sauce all over the chicken. Flip the chicken and set it over direct heat. Grill until richly glazed, about 1 minute. Turn the chicken skin side up and grill until glazed, about 1 minute longer. Let the chicken rest for 15 minutes. Serve with the remaining sauce and the mango slices.
Any leftover adobo rub can be stored at room temperature for up to a month.