Wash and dry all produce. Trim, then thinly slice scallions, keeping greens and whites separate. Mince garlic. Core and seed poblano, then cut into ½-inch squares. Drain and rinse beans.
Heat a drizzle of oil in a large pan over medium-high heat. Add turkey, breaking it up into pieces. Cook, tossing occasionally, until browned at the edges and no longer pink, 5-6 minutes. Season with salt and pepper. Remove from pan with a slotted spoon and set aside.
Remove pan from heat and carefully pour out and discard any excess grease left by turkey. Return to medium-high heat and add scallion whites, poblano, and garlic. Cook, tossing, until lightly browned and softened, 5-6 minutes.
Add chili powder to pan and toss to coat veggies. Cook until fragrant, about 30 seconds. Season with salt and pepper.
Add stock concentrate, beans, tomatoes, beef, and 1 cup water to pan and stir to combine. Bring to a boil, then lower heat and let simmer until thick and stew-like, about 10 minutes. Let it simmer longer for a stronger flavor. Season with salt and pepper.
Divide chili between bowls. Sprinkle with cheddar and scallion greens. Dollop with sour cream and serve.