For the broth:
1 3- to 4-pound whole chicken, halved
1 medium yellow onion, quartered
8 cloves garlic
2 teaspoons black peppercorns
4 whole cloves (or 1/4 teaspoon ground allspice)
8 allspice berries (or 1/4 teaspoon ground allspice)
2 cinnamon sticks (or 1/2 teaspoon ground cinnamon)
1 leafy stem of cilantro
1 teaspoon salt, plus more to taste

For the soup:
Oil for frying
4 corn tortillas, cut into strips
1 medium yellow onion, quartered
10 cloves garlic
1/2 teaspoon ground cumin
1/2 teaspoon oregano
1 cup chopped cilantro, divided
Pinch of cayenne
2 teaspoons lime zest
Salt and black pepper to taste
1/4 cup lime juice
1/2 cup shredded Monterrey Jack (4 ounces)
2 jalapeños, stems and seeds removed, diced
1 avocado, pitted and peeled, cubed
1 lime, cut into slices