Peel, rinse, core and quarter tomatillos. In a food processor, process tomatillos, jalapeño pepper and canned green chiles until smooth. You'll probably have to do two batches. Set aside.
Heat 2 tablespoons olive oil in a large, deep sauté pan over medium-high heat. Add chicken and season with salt and pepper. Cook, stirring occasionally, until no longer pink, about 6 minutes. Transfer to a bowl and set aside.
Reduce heat to medium and sweat onion, drizzling in more oil, if needed. Stir frequently to avoid browning and cook until softened 4 to 5 minutes.
Add garlic and cook, stirring constantly, until fragrant, about 45 seconds. Add ground turkey, breaking up with a wooden spoon and stirring to combine with aromatics. Sprinkle cumin, chili powder, coriander and oregano over turkey and stir to combine. Continue cooking until turkey is mostly cooked through, 5 to 6 minutes, stirring occasionally.
Add tomatillo sauce and chicken broth to pan, stirring to combine. Stir in cannellini beans and bring to a boil. Reduce heat, cover and simmer for at least 45 minutes, stirring occasionally, until flavors have melded together nicely. Taste and adjust seasoning with salt and pepper.
You can serve it now, garnishing with chopped cilantro, if you like. But if you chill it overnight and reheat it, the flavors will really develop.