Heat 2 cups chicken broth in a saucepan until it begins to simmer, about 5 minutes. Pour broth into a blender. Toast challah bread pieces and tortilla strips in a dry pan over medium heat, stirring constantly, until lightly browned, about 3 minutes. Transfer to the blender with chicken broth and chiles. Allow the chiles, bread and tortillas to soak, fully submerged, in the chicken broth until softened, about 10 minutes. Blend the mixture until smooth.
Cook tomatoes and tomatillos in a dry skillet on medium-high heat until soft and blackened, 3–4 minutes per side. Add to the blender with the chile purée.
Heat olive oil in a pan and stir in onion, garlic, pecans, raisins, cumin, thyme, cinnamon, cloves, and allspice berries. Cook and stir until onions are soft and golden, 5–8 minutes. Remove the cinnamon sticks and other whole spices; add onion mixture to the blender with the chile-tomato mixture and blend until smooth.
Pour chile purée into a large saucepan over medium heat. Stir in chocolate, chicken broth, sugar, and salt. Bring mixture to a simmer, stirring until chocolate is melted and sauce is thickened and slightly reduced, 10–15 minutes. Cook meatballs as desired and toss in sauce until well covered. Serve over rice or with toothpicks as an appetizer