Start by heating the olive oil in a wide skillet over medium-high heat. Add the carrots, celery, potato, and onion. Cook until the vegetables are softening and the onion is becoming translucent, which should take about 6 to 8 minutes. Stir in the poultry seasoning, salt, and pepper, and cook for an additional 30 seconds to allow those flavors to meld.
Transfer the sautéed vegetables to the bottom of your slow cooker. Pour in the chicken broth, then place the chicken breasts in a single layer on top. Sprinkle the remaining salt over the chicken.
Cover the slow cooker and cook on low for 2 to 3 hours, or until the chicken is fully cooked and registers 165°F on an instant-read thermometer. Once cooked, carefully transfer the chicken to a cutting board and turn off the slow cooker.
Prepare the dumplings: In a mixing bowl, whisk together the all-purpose flour, white whole wheat flour, baking powder, salt, and garlic powder. Gradually pour in the milk and stir until combined. The batter should be thick and able to hold its shape. Allow it to rest for at least 5 minutes.
In the same skillet used for the vegetables, melt the butter over medium heat. Once melted, sprinkle the flour on top and whisk continuously until the mixture turns golden brown, about 30 seconds to 1 minute.
Slowly pour in the milk a little at a time, whisking to eliminate lumps. Bring this mixture to a gentle boil, whisking until it thickens, which should take about 3 minutes.
Pour the thickened milk mixture into the slow cooker and stir to combine with the chicken and vegetables. Add the frozen peas and mix well.
Once the chicken has cooled, dice it into bite-sized pieces and return it to the slow cooker, mixing it in with the rest of the ingredients.
Set the slow cooker to HIGH. Scoop the dumpling batter by tablespoons and drop it on top of the soup, spreading the scoops evenly to cover most of the surface.
Cover the slow cooker again and cook on HIGH for an additional hour, checking for doneness by cutting a dumpling in half; it should be moist but not raw inside. Finish by sprinkling some fresh parsley or thyme over the top.
To serve, scoop down through the dumplings to get some soup and dumplings in every bowl. Enjoy this comforting dish hot!
