Add the olive oil to a large, heavy-bottom pot set over medium heat. Once the oil is warm, add the minced garlic, diced onions and diced peppers and cook, stirring frequently, until the vegetables are soft, about 5 minutes. Add the tomato paste and cook, stirring, until caramelized, about 2 minutes.
Add the ground cumin, chili powder, pinto beans (with chili sauce), kidney beans, crushed tomatoes and brown sugar to the pot, stirring to combine. Add the chopped turkey, reduce the heat to low, and cook, stirring occasionally, until warmed throughout, about 10 minutes.
Serve the chili topped with sour cream, avocado, cheddar cheese and scallions.