Add butter to your large pot.
Heat it over medium heat.
Add onions, carrots, and celery.
Cook for 5 minutes until softened.
Add garlic and cook 1 minute more.
The vegetables should smell wonderful.
Add chicken breasts to the pot.
Pour in broth and water.
Bring everything to a boil.
Reduce heat and simmer 20 minutes.
The chicken should be fully cooked.
Remove chicken and shred it.
Set aside for later use.
Mix gluten-free flour, baking powder, and salt.
Whisk milk, egg, and melted butter together.
Combine wet and dry ingredients gently.
Don't overmix the batter. It should be slightly lumpy.
Return shredded chicken to the pot.
Add frozen peas now. Bring the mixture to a simmer.
Drop spoonfuls of dumpling batter on top.
Cover the pot with a lid.
Cook for 15 minutes without lifting the lid.
Dumplings will puff up beautifully.
Check if dumplings are cooked through.
They should be fluffy and tender.
Season with salt and pepper.
Stir gently to combine everything.
Let it rest 5 minutes before serving.