Trim, chop and rinse leeks. Chop bell pepper. Mince garlic. Peel, seed and cut into 1-inch cubes the butternut squash. Cut turkey into 1/2-by-2-inch strips.
Heat oil in a Dutch oven over medium-high heat. Add leeks and bell pepper; cook, stirring often, until the vegetables begin to soften, 3 to 4 minutes. Add garlic and cook, stirring, for 1 minute more. Stir in broth, squash, thyme and cumin; cover and bring to a boil. Reduce heat to medium-low and cook until the vegetables are tender, about 10 minutes.
Add turkey and corn; return to a simmer and cook until the turkey is just cooked through, 3 to 4 minutes. Add lime juice and crushed red pepper. Season with salt and pepper.