Heat the oil in a large skillet over medium heat, then add the chopped onion, yellow pepper, and minced garlic. Cook for about five minutes, stirring occasionally, until everything has softened and turned fragrant.
Stir the cumin, oregano, and chili powder directly into the skillet with the softened vegetables. Let everything cook together for about a minute, which helps the spices release more of their flavor before they hit the slow cooker.
Scrape the sautéed vegetable and spice mixture straight into your slow cooker insert. This little step of blooming everything on the stove first makes a noticeable difference in the final depth of flavor.
Pour in the black beans, cooked turkey, pumpkin puree, diced tomatoes, and chicken broth. Give everything a good stir so the pumpkin fully dissolves into the broth instead of clumping at the bottom.
Cover the slow cooker and set it to low for 7 to 8 hours. Resist the urge to lift the lid too often, since every peek lets out heat and adds extra cooking time.
Once the chili has thickened and the flavors have melded, give it one final stir before ladling it into bowls. Add whatever toppings you like and dig in while it's still steaming hot.