In a large stock pot or dutch oven, add 2 tablespoons of the butter and olive oil. Melt over medium-high heat, and then add the ground turkey. Cook until brown and cooked through, about 8-10 minutes. Remove the meat with a slotted spoon and set aside. Keep the burner turned on.
Add the remaining tablespoon of butter, if needed, and melt over medium-high heat. Add the onion, peppers and carrots. Cook until the veggies are tender, about 8-10 minutes. Next add the mushrooms and cook for 4-5 minutes or until they are brown and have released all of their liquid. Next add the garlic, and cook for an additional 2 minutes.
Season the veggie mixture with brown sugar, cumin, chili powder, herbs de provence, smoked paprika and salt and pepper to taste. Mix to combine.
Add the pale ale beer and the chicken broth and bring the chili to a rolling boil. Reduce the heat to medium-low and simmer, uncovered, for 25-30 minutes.
Increase the heat back up to medium, and add the already cooked turkey, diced tomatoes, all of the beans and the frozen corn. Stir to combine and cook for an additional 10 minutes or until the entire chili is warmed through.
Adjust seasoning to taste.
Keep warm on the stove, covered, until you are ready to serve.
Top with sour cream, avocado, chopped cilantro, chopped chives and/or grated cheddar cheese.