Place chicken breasts in a single layer in a 6-quart (or larger) slow cooker. Sprinkle with 1/4 teaspoon kosher salt and 1/4 teaspoon black pepper. Cover and cook on LOW until the chicken reaches 165°F, about 1 1/2 to 2 hours.
While the chicken cooks, melt the butter in a medium saucepan over medium heat. Sprinkle the flour over the butter and whisk until combined; continue whisking and cooking for at least 1 minute until the flour turns golden and smells nutty.
Gradually whisk in the milk and chicken broth until smooth. Stir in 1/4 teaspoon kosher salt, 1/4 teaspoon black pepper, Parmesan, poultry seasoning, Italian seasoning, and garlic powder. Cook, stirring constantly, until the sauce thickens, about 3 to 5 minutes. Remove from heat.
Toast the 2 slices of whole grain bread deeply in a toaster or in a 350°F oven for 8 to 10 minutes, turning once, until very dry and deep golden. Let cool.
When the chicken is done, transfer it to a bowl and discard any cooking liquid; wipe the slow cooker clean. Shred the chicken with two forks, your fingers, or a hand mixer.
Pour the thickened sauce over the shredded chicken in the slow cooker or bowl. Crumble or pulse the toasted bread into small pieces and add to the chicken. Stir in the Greek yogurt until combined.
Cover and cook on LOW for 1 hour. Uncover and stir well just before serving.
To serve, pile the chicken onto whole grain buns and top with shredded cheese if using. For open-faced sandwiches, place chicken on toasted bread and brown the cheese under the broiler if desired.
