Sauté the veggies: In a large pot, heat olive oil (or vegetable broth for oil-free) over medium heat. Add the diced onion and carrot, and cook for 5-7 minutes until softened. Add the minced garlic and sauté for another minute until fragrant.
Add the beans and tomatoes: Stir in the kidney beans, diced tomatoes (with juice), tomato paste, and coconut sugar.
Season: Add the chili powder, cumin, smoked paprika, salt, and pepper. Stir to combine all the ingredients well.
Simmer: Bring the mixture to a boil, then reduce the heat and let it simmer for about 20-25 minutes, stirring occasionally, until the chili thickens and the flavors meld together.
Serve: Adjust the seasoning to taste, and serve hot! You can top the chili with avocado slices, vegan sour cream, or fresh cilantro if desired.