Make the spice mix: Mix ancho chili powder, paprika, cumin, salt, chipotle pepper, oregano, cocoa powder, black pepper, cayenne pepper, and cinnamon in a bowl; set aside.

Make the chili: Heat olive oil in a large, heavy pot over medium heat. Stir in onion; cook and stir until onion has softened and turned translucent, about 5 minutes. Stir in ground turkey and garlic. Cook and stir until turkey is no longer pink, breaking up any large chunks, 7 to 8 minutes. Stir in spice mixture. Cook until fragrant, 3 to 4 minutes.

Stir in tomato purée and water. Bring to a simmer, then reduce heat to low. Cook until turkey meat is broken down, about 1 hour. Stir in beans, and continue to simmer until flavors have blended, 20 to 30 more minutes.