In a large, heavy-bottomed pot, heat a drizzle of olive oil over medium heat. Add the onion, season with salt, and cook until the onion starts to sweat and become translucent, 3 minutes. Add the garlic and cook until fragrant, 2 minutes more.
Add the parsnips and butternut squash and season with salt, paprika, oregano, cumin, allspice, and chipotle powder. Stir to coat the vegetables with the spices. Cover and cook for 20 minutes, stirring occasionally to prevent sticking, until the vegetables begin to soften.
Add the cannellini beans, cilantro, and vegetable broth. Increase the heat to medium-high and bring to a boil for 2 minutes. Reduce the heat to medium-low and simmer for 15 minutes, until the chili is thickened and the vegetables are cooked through.
Ladle the chili into bowls and top with cilantro and cheddar cheese.