In a large skillet over medium-high heat, warm the olive oil. Once shimmering, add the ground turkey and cook, breaking it up, until it's no longer pink and lightly browned, about 5 to 7 minutes.

Stir in the chopped onion, jalapeño, garlic, chili powder, 1 tsp of the kosher salt, and black pepper. Sauté until the onions are softened and fragrant, about 5 minutes.

Add in the tomato paste, stirring frequently until it darkens slightly and begins sticking to the pan; this step is key for deepening the flavor, taking about 2 to 3 minutes.

Pour the turkey mixture into a 5 to 6-quart slow cooker. Add the water, black beans, kidney beans, and diced tomatoes (with their juices), along with the remaining 2 tsp of salt. Stir well to combine.

Cover and cook on Low for 6 to 7 hours or on High for 3 to 4 hours.

Before serving, stir the chili well. If you prefer a thicker consistency, remove the lid for the last 30 minutes of cooking or continue cooking uncovered on High until reduced to your liking.