Arrange the chicken breasts in a single layer in a 6-quart (or larger) slow cooker; season with additional salt and pepper. Cover and cook on LOW until 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 in the flour and whisk constantly until the flour turns golden and smells nutty, at least 1 minute.
Gradually whisk in the milk and chicken broth, then stir in 1/4 teaspoon kosher salt, 1/4 teaspoon black pepper, Parmesan, poultry seasoning, Italian seasoning, and garlic powder. Cook, stirring, until the sauce thickens, about 3–5 minutes, then remove from heat.
Deeply toast the two slices of whole grain bread in a toaster or in a 350°F oven for 8–10 minutes, turning once, until very golden and dry. Let cool, then tear or crumble into small pieces.
When the chicken is done, transfer it to a bowl and discard any cooking liquid; wipe the slow cooker clean with a paper towel. Shred the chicken with two forks, your fingers, or a hand mixer.
Pour the thickened sauce over the shredded chicken in the slow cooker. Add the torn/crumbled toasted bread and the Greek yogurt, then stir thoroughly to combine.
Cover and cook on LOW for 1 hour to meld flavors. Uncover, stir before serving, and adjust seasoning if needed.
To serve, pile the creamy shredded chicken onto whole grain buns and top with optional shredded cheese; for open-faced sandwiches, place chicken on toasted bread and melt cheese under a broiler if desired.