Roast the unpeeled garlic on a griddle or heavy skillet set over medium heat for about 15 minutes, turning frequently, until blackened outside in spots and soft inside. Remove, cool, then slip off the skin.
Place the black pepper, allspice, cloves, cumin and oregano into a molcajete (or washable electric spice mill) and pulverize thoroughly. Add the peeled garlic cloves, vinegar and 1/2 teaspoon salt, and pound (or process) into a paste.
Place the chicken thighs in a bowl and scoop in 1/2 of the spice paste. Mix everything together until the chicken is well coated.
Heat a grill pan over medium (or light a charcoal fire and let burn until the coals are covered with gray ash and the grates are medium hot). Place the chicken skin-side down on the grill pan (or charcoal grill). When crispy-brown underneath (about 10 minutes), turn the chicken and continue grilling until the chicken is done (about 15 minutes more). Transfer to a baking sheet and keep warm in a low oven.
Roast the banana pepper over an open flame until blistered and blackened all over. Cool. Peel, seed and slice the peppers 1/4-inch thick.
Heat the oil in a large (10-inch) skillet over medium. Add the onions and chiles and cook until the onion begins to brown, about 7 minutes. Add the remaining spice paste, the chicken broth, vinegar and 1/2 teaspoon salt. Stir to combine and simmer gently over medium-low heat until about half of the liquid is reduced, about 15 minutes.
Spoon the onions and chiles over the bottom of a large platter. Pile the grilled chicken on top. Pour the escabeche juices over the chicken and garnish with pickled red onions and chopped cilantro.