Melt the butter on low in a large pot or Dutch oven. Add the onion and leek along with a pinch of salt and saute until very soft, about 15 minutes. Stir in garlic and saute for about 30 seconds.
Add the flour, increase the heat to medium, and stir with a whisk for 2 minutes.
Pour in the stock and whisk as it comes to a simmer and starts bubbling. Simmer the stock for 30 minutes, whisking as needed. (Mix the batter now.)
Add the carrots, celery, salt, pepper, thyme, and bay leaf. Bring back to a simmer.
Add the cream and diced chicken.
Once the soup has come back to a simmer, drop in the biscuits in generous tablespoon sized amounts into the soup.
Reduce the heat to low, cover, and cook for 10-12 minutes, or until the dumplings are fluffy and cooked through.
Taste and adjust the seasonings as needed. Serve with extra chopped chives over the top.