Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat.
Add the diced onion, bell pepper, and jalapeño. Sauté for 5 to 7 minutes until the vegetables are softened and the onions are translucent.
Stir in the minced garlic and cook for 1 minute until fragrant.
Add the ground turkey to the pot. Cook while breaking into small crumbles with a wooden spoon until browned and no longer pink.
Create a small well in the center of the meat mixture and add the tomato paste, chili powder, cumin, smoked paprika, oregano, salt, and pepper. Stir for 1 to 2 minutes to bloom the spices and caramelize the paste.
Pour in the fire-roasted tomatoes (with juices), chicken broth, kidney beans, and black beans. Stir thoroughly to combine.
Bring the mixture to a boil, then immediately reduce the heat to low. Cover partially and simmer for 30 to 45 minutes, stirring occasionally, until the chili has thickened to your desired consistency.
Taste and adjust seasoning with additional salt or pepper if needed before serving.