Mix the ancho chile powder, paprika, cumin, salt, chipotle pepper, oregano, cocoa powder, black pepper, cayenne pepper, and cinnamon in a bowl; set aside.
Heat the olive oil in a large heavy pot over medium heat. Stir in the onion; cook and stir until the onion has softened and turned translucent, about 5 minutes. Stir in the ground turkey and garlic. Cook and stir until turkey is no longer pink, breaking up any large chunks, 7 to 8 minutes. Stir in the spice mixture. Cook until fragrant, 3 to 4 minutes.
Stir in the tomato puree and water. Bring to a simmer, then reduce heat to low. Cook until the turkey meat is broken down, about 1 hour. Stir in the beans, and continue to simmer until flavors have blended, 20 to 30 more minutes.