Heat the olive oil in a Dutch oven or other large pot over medium. Lift the pot from side to side to coat the bottom evenly with oil; once hot, add the ground bison and sauté, making sure to break up the bison into small pieces, until browned, about 10 minutes. Transfer to a plate to rest.
Add the onion and garlic; and cook until slightly softened, about 3 minutes. Then stir in the sugar and spices and cook for another 2 minutes. Add the tomato, stock and bison back to the pot. Bring to a simmer and cook, covered, until the meat is tender, about 1 hour.
Stir in the white beans and green beans and cook, covered for about 15–20 minutes longer.
Serve with the *optional* warm polenta in a wide bowl with the bison and bean chili spooned over the top. Garnish with the crumbled cheese and scallions.