In a large skillet over medium-high heat, heat the olive oil. Add the turkey, onion, bell pepper, salt, and pepper once the oil is hot and shimmering. Cook, breaking up the meat, for about 8 minutes, or until the turkey is cooked through and most of the excess liquid has evaporated. Cook until the chili powder, cumin, and cayenne are fragrant about 30 seconds.

Combine the black beans, pinto beans, diced tomatoes in their juices, and carrots in a mixing bowl. Cook, occasionally stirring, for about 5 minutes, or until the tomatoes have broken down and most of the liquid has evaporated. Turn off the heat. Season with salt and pepper to taste.

Coat a 5-quart or larger slow cooker lightly with nonstick spray. 1 1/2 cups of the turkey-bean mixture, spread evenly on the bottom. Top with 2 tortillas, spreading them out to cover the beans and overlapping them in the center as needed. Sprinkle with 1/2 cup shredded cheese. Layer as follows: 1 1/2 cup beans, 1/2 cup cheese, 2 tortillas, 1 1/2 cup beans, 2 tortillas, 1/2 cup cheese, and remaining beans. Save the remaining 1/2 cup cheese for sprinkling on top.

Cook for 4 to 5 hours on low or 2 to 3 hours on high, until heated