Place the olive oil and chopped onion and pepper into a large pot along with the olive oil. Cook over medium heat until the vegetables start to soften, about 5 minutes.
Add the sliced mushrooms and ground turkey, and raise the heat to medium high. Cook until the turkey is brown. Use a large spoon or spatula to break up the turkey as you cook it.
Add the pumpkin puree, tomatoes, and black beans and their juice. Stir. Add the spices and salt and pepper, and stir well.
Raise the heat and bring the chili to a boil, then reduce to a simmer. Simmer for about 20 minutes.
Serve with cornbread or green salad. Add your choice of toppings if desired - try tortilla chips, guacamole, or green onions.
Notes
Store leftover chili in the refrigerator for up to four days.You can freeze the leftovers if you like - freeze in individual sized containers for up to three months.