Heat olive oil in a large Dutch oven or heavy-bottomed soup pot over medium-high heat. Season chicken pieces with a pinch of salt and pepper, then add to the pot in a single layer. Cook 3-4 minutes per side until golden brown, then transfer to a plate (they will finish cooking in the broth).

Reduce heat to medium. Add onion, celery, and carrots to the pot and cook, stirring occasionally, until softened, about 5 minutes. Stir in garlic and cook 1 minute more until fragrant.

Pour in chicken broth, add thyme and bay leaf, and return the chicken along with any juices to the pot. Bring to a boil, then reduce heat to medium-low, cover, and simmer for 10 minutes to marry the flavors. Season with salt and pepper to taste.

While soup simmers, whisk flour, baking powder, and ¾ tsp salt in a medium bowl. Add cold butter cubes and cut in with a pastry cutter or fingertips until mixture resembles coarse meal with pea-sized butter pieces. Stir in chives and parsley. Pour in cold milk and stir with a fork just until a shaggy dough forms—do not overmix.

Remove bay leaf from soup. Using a spoon or small cookie scoop, drop rounded golf-ball-sized portions of dough (about 2 tablespoons each) onto the simmering soup surface, spacing them evenly. You should get 10–12 dumplings.

Cover the pot tightly and simmer over medium-low heat for 15 minutes, without lifting the lid. The dumplings will cook through and double in size. Check one dumpling by cutting in half—it should be fluffy and dry inside. Ensure chicken pieces have reached an internal temperature of 165°F (74°C) using an instant-read thermometer. Let soup rest uncovered for 5 minutes before serving.