Starting with the stew: Use paper towels to dry the chicken first, then season with your salt and pepper. Be generous here. Now heat 2 teaspoons of your oil in a study-bottomed pot (think Dutch oven or cast iron pan for best results.). Heat over medium-high heat until smoking. Water should instantly boil when splashed onto the surface! Add just half of the chicken and cook for about 10 minutes, you'll see it golden brown on both sides.
Take the chicken off the pot and removed the skin. You'll pour off the chicken fat and reserve (can save for later!). Now, put the pot back onto medium-high heat and repeat with teh remaining oil and chicken.
After pouring off any excess chicken fat, add the butter to your pot and melt over medium-high heat. Add your aromatics now (leeks, onion, and 1/4 teaspoon salt). Cook these until they are softened, about 7 minutes.
Now we can add in in the flour abndwWhisk in the sherry. Make sure to scrape up any browned bits- that's where the flavor is! Stir in the broth, milk, thyme, and bay leaves.
Add your chicken back into the pot with any juices it may be resting in. Cover your pot and let simmer so the chicken is fully cooked and tender. This'll be about an hour.
Once done, take the chicken out and onto a cutting board. You don't need the bay leaves, so toss those out. You will want to chicken to "rest" for a few minutes. Once rested, shred up the chicken, get rid of the bones. After, grab a wide spoon to skim the fat from the surface of the sauce in the pot. Then add the chicken back to the stew.
To Make The Dumplings: Stir your baking powder, flour, and salt together for your dry ingredients. Combine your milk and fat in a microwave-safe bowl and warm it up in your Microwave for just a minute. Combine the wet ingredients with the dry, mixing with a wooden spoon until incorporated and smooth.
Before we add the dumplings to the stew, get the stew back to a simmer and add in your peas and tarragon. Season with salt and pepper to taste. Here's where you'll drop golf-ball-sized dumplings over the top of the stew. Make sure these dumplings are spaced about 1/4 inch apart. This will give you about 18 dumplings.
Lower the heat to low and cover the stew. Cooking everything until the dumplings have about doubled in sized, about 15-18 minutes. And serve!
Note On Finishing Dumplings: Scoop a golf-ball-sized portion of the dumpling batter onto a soup spoon. You'll want to use a second spoon to slide the dumpling batter into the stew (giving it a football-like shape). Cover the stew with about 18 dumplings, leaving about 1/4 inch between each because they will grow. When fully cooked, the dumplings will have doubled in size.