Add ground turkey to the pot. Cook until it's completely cooked through and no longer pink, breaking it up into small pieces with a spoon and stirring occasionally. Season generously with salt and pepper as it cooks.
Once the turkey is browned, stir in the 3 tablespoons of chili powder, the chipotle peppers, the diced jalapeño and poblano peppers, and the 1 tablespoon of adobo sauce. Stir everything together for about a minute, letting the spices bloom.
Pour in the 1/2 cup of chicken stock, the 14 1/2 ounces of kidney beans (drained and rinsed), and the 28 ounces of canned tomatoes. Stir to combine, then bring the mixture to a gentle simmer.
Cover the pot, reduce the heat to low, and let the chili cook for at least 1 to 2 hours, stirring occasionally to prevent sticking. Before serving, taste and adjust the seasoning with more salt, pepper, or chili powder if needed.