Heat 2 tbsp olive oil in a large Dutch oven over medium-high heat.
Season chicken thighs with salt and pepper. Brown chicken for5 minutes per side until golden. Remove chicken and set aside.
Add diced onion, sliced carrots, and chopped celery to the pot. Sauté vegetables for 6 minutes until softened. Add minced garlic and cook for 1 minute until fragrant. Pour in 6 cups chicken broth, scraping any browned bits from the bottom. Add 1 tsp dried thyme and 1 bay leaf.
Return chicken to the pot. Bring to a boil, then reduce heat to low. Cover and simmer for 25 minutes until chicken is cooked through.
Remove chicken and shred with two forks. Return shredded chicken to the pot. Stir in 1 cup frozen peas.
In a separate bowl, whisk together 2 cups flour, 1 tbsp baking powder, and 1 tsp salt. Combine 1 cup milk and 3 tbsp melted butter in another bowl. Pour wet ingredients into dry ingredients and stir until just combined.
Drop tablespoon-sized dumplings directly into the simmering broth. Cover and cook for 15 minutes without peeking, this keeps the dumplings fluffy. Remove bay leaf before serving.