Prepare the Aromatics : Begin by dicing the yellow onion and poblano pepper, and mincing the garlic cloves. Set them aside, ready for the pot.
Brown the Turkey : In a large, heavy-bottomed pot or Dutch oven over medium heat, add the ground turkey. Cook, breaking it apart with a spatula, for 7 to 8 minutes, until it is thoroughly browned and no pink remains. Drain off any excess fat.
Sauté Vegetables : Add the prepared onion and poblano pepper to the pot with the browned turkey. Continue to cook, stirring frequently, for about 5 minutes, or until the vegetables have softened slightly. Stir in the minced garlic and cook for another minute until fragrant.
Bloom the Spices : Sprinkle the chili powder, cumin, granulated garlic, smoked paprika, salt, and pepper directly into the pot. Stir constantly for 45 seconds to toast the spices and awaken their flavor.
Load the Slow Cooker : Carefully transfer the entire contents of the Dutch oven into the basin of a 6 or 7-quart slow cooker.
Add Liquids and Beans : Pour in the crushed tomatoes, chicken broth, and all three cans of rinsed beans. Stir everything together until well combined.
Simmer and Meld : Secure the lid on the slow cooker. Set the temperature to LOW and allow the chili to cook for 5 hours, giving the flavors ample time to meld into a rich and hearty stew.
Final Touches and Serving : Once cooked, give the chili a final stir. Serve hot in bowls, garnished with a sprinkle of fresh cilantro, a dollop of Greek yogurt, and a fresh lime wedge on the side for squeezing.