Pour the oil into a 4 or 5 quart soup pot or Dutch oven and place over medium heat. Add the onion, carrots and celery and cook until the vegetables are softened, stirring occasionally.
Add the garlic and all the spices through the black pepper, stirring to coat in the oil. Add the turkey and cook until it's no longer pink, stirring and breaking the meat up with a spoon, about 8 minutes.
Add the herbs, pumpkin, beans, broth and 2 teaspoons salt. Bring to a simmer, partially cover and cook 25 minutes, adjusting the heat so it doesn't boil.
Remove from the heat and stir in the cream. Taste and adjust the seasoning, if needed. Serve in bowls.
To make this chili in a Crockpot or slow cooker:
Follow step 1 and 2. Transfer the mixture to your slow cooker and add the herbs, beans, pumpkin, 1 1/2 cups broth and salt.
Set to cook on low for 6 hours or 3 hours on high.
Stir in the cream and serve.
To make in a pressure cooker:
Set your pot to Saute. Follow the steps in step 1 and 2.
Add the remaining ingredients except the cream to the pot as in step 3.
Cover and set to pressure cook for 10 minutes, allowing pressure to release naturally.