Pennsylvania Dutch Potato Filling

Name: Pennsylvania Dutch Potato Filling
Ingredients: 7 tablespoons unsalted butter, divided; 1 cup whole milk; 2 large eggs; About 10 ounces potato sandwich bread (8 to 9 slices, about 1/2 loaf); 3 pounds russet potatoes; 2 tablespoons kosher salt, divided; 1 medium yellow onion; 2 large stalks celery; 3 cloves garlic; 5 sprigs fresh parsley; 8 large or 12 medium fresh sage leaves; 2 sprigs fresh thyme; 1 teaspoon freshly ground black pepper, divided; 1/2 cup plus 1 tablespoon low-sodium chicken broth, divided, plus more as needed; 1/2 teaspoon salt-free poultry seasoning