In a large dutch oven, heat olive oil over medium-high heat. Add chicken breasts and brown for 3 minutes per side. Remove from pan and keep warm while you saute the veggies.
Add onion and carrots to the pan, cook for 3 minutes. Add garlic and cook for 1 minute.
Deglaze pan with hard cider. Add chicken, broth, thyme and bay leaf. Return the chicken to the pan, reduce heat to medium-low and simmer for 20 minutes.
Make the dumpling batter. While the soup is simmering prepare the dumpling batter by mixing flour, salt and paprika in a medium bowl. Add the butter and using a fork or pastry cutter, mix into flour mixture. Add egg and buttermilk and mix until a stiff, sticky dough forms.
Once you've finished making the dumpling dough remove the chicken from the pan and shred or chop into bite-sized pieces. Add the chicken and peas to the soup and stir to incorporate.
Add the dumplings. Using a kitchen teaspoon, drop large spoonfuls of the dumpling batter into the simmering soup until the pot is full or all of the dumpling batter has been used.
Cover and simmer for 10 minutes or until the dumplings are cooked (they will be firm to the touch when done).
Remove the bay leaf and serve.