Heat olive oil in a large pot over medium heat. Add diced onion and carrot and sauté for 5 minutes until softened. Stir in minced garlic and cook for 1 minute until fragrant. Can use an Instant Pot - set to saute.
Add ground turkey to the pot and cook until browned, breaking it up with a spoon as it cooks. Stir in chili powder, cumin, oregano, smoked paprika, salt, and black pepper. Cook for 1-2 minutes to toast the spices.
Mix in tomato paste and cook for another minute. Add diced tomatoes, kidney beans, chickpeas, edamame, corn, and chicken broth. Stir to combine.
Bring the chili to a boil, then reduce heat to low. Cover and simmer for 30-45 minutes, stirring occasionally, until the flavors meld and the chili thickens. Or if you are using an Instant Pot - set to slow cook on high for a few hours.
Serve hot, garnished with fresh cilantro and your favorite toppings.