In a skillet, heat olive oil over medium heat. Add onion and garlic and sauté until fragrant. Transfer to the slow cooker.
Place chicken thighs over the onions. Add carrots, celery, seasonings, and chicken broth. Cover and cook on low for 5 to 6 hours.
Once tender, remove the chicken and shred with two forks. Return it to the slow cooker.
Whisk 1 tablespoon flour into the cream, then stir into the soup base. This will help thicken the broth slightly.
In a bowl, combine flour, baking powder, salt, and butter. Use a pastry cutter or your fingers to work in the butter until the mixture resembles crumbs.
Stir in milk and parsley just until combined.
Drop spoonfuls of dough (about 1 tablespoon each) on top of the hot soup. Cover and cook on high for another hour, or until the dumplings are cooked through and fluffy.
Spoon into bowls and garnish with a bit more parsley.
