Melt butter in a pot over medium heat. Add garlic; cook and stir until fragrant, about 1 minute. Whisk in 1/4 cup flour gradually. Pour in chicken broth slowly; add poultry seasoning, 1 tablespoon salt, and pepper. Whisk in cream of chicken of soup; bring to a boil.
Stir turkey, carrots, turkey gravy, peas, and celery. Reduce heat to low; cook until heated through, about 5 minutes.
Preheat oven to 375 degrees F (190 degrees C). Spray a large casserole dish with cooking spray.
Pour turkey mixture into the prepared dish.
Place 2 cups flour, milk, shortening, baking powder, and 1/2 teaspoon salt in a blender. Blend until mixture forms a ball, adding pinches of flour if too doughy. Roll dough into small balls by hand; place balls 1/2-inch apart on top of the turkey mixture.
Bake until top is lightly browned, about 20 minutes. Let cool until dumplings are set, 5 to 10 minutes.
