To prepare the shredded chicken in the slow cooker, arrange the breasts in a single layer in a 6-quart or larger slow cooker. Sprinkle with salt and pepper. Cover and cook on LOW for 1 and a half to 2 hours, until the chicken reaches 165°F on an instant-read thermometer. If you're using a different size of breasts or swapping for chicken thighs, refer to my post for Crock Pot Shredded Chicken for specific cooking times.
While the chicken cooks, melt the butter in a medium saucepan over medium heat. Sprinkle the flour over the top. Whisk to combine, then continue whisking and cooking until the flour turns golden brown and smells slightly nutty, which should take at least one full minute. It's essential to cook the flour thoroughly to avoid a raw taste in the final dish.
Gradually add the milk and broth, whisking constantly to smooth out any lumps. Stir in the kosher salt, black pepper, Parmesan, poultry seasoning, Italian seasoning, and garlic powder. Keep cooking and stirring until the mixture thickens a bit more, which should take about 3 to 5 minutes depending on the size of your pan. Once it reaches the desired thickness, remove it from the heat.
Deeply toast the bread in your toaster, or place it in a 350°F oven for 8 to 10 minutes, turning it over halfway through. The bread should be a deep golden brown, dry, and just on the verge of being burned without crossing the line. Let it cool completely.
Once the chicken has finished cooking, transfer it to a bowl. Discard any remaining cooking liquid and carefully wipe the slow cooker clean with a paper towel. Shred the chicken using two forks, your fingers, or for maximum ease, use a hand mixer and shred it right in the crock pot. If you're using pre-cooked chicken, add it to the slow cooker now.
Pour the thickened sauce over the shredded chicken in the slow cooker. Tear and crumble the toasted bread into small pieces directly over the top. You can also pulse it into crumbs in a food processor, but I find using my fingers is just as simple. Add the Greek yogurt and use a large spoon to stir everything together until well combined.
Cover the crockpot again and let it cook on low for an additional hour. Just before serving, uncover and give the chicken a good stir to mix everything thoroughly.
To serve, pile the chicken mixture onto buns and top with your choice of cheese. Alternatively, serve it open-faced over the toasted bread, adding the cheese on top. If you like, you can pop the bread under the broiler for a few moments to melt and brown the cheese. Enjoy!