In a large stockpot, melt butter over medium low heat. Add the flour and white pepper and mix with a wooden spoon until a thick paste will forms. Let this get a toasty brown. Slowly add the chicken stock a little at a time to make the roux. This will act as a base and thickener for the stew.
While the roux is slowly cooking add the white wine, tarragon and onion, stir and start the chicken and vegetables poaching.
In a large saucepan add the chopped chicken, carrots and celery. Add enough water to barely cover, place a lid on and bring to a boil. Lower heat and poach for 10 minutes.
Add the mustard to the roux and stir to incorporate thoroughly. Next, add the drained chicken and vegetables, along with the broth and cream, to the roux mixture and stir.
Add the frozen peas if desired at this point and let this simmer on low to meld the flavors and add the dumplings.
Mix the Bisquick, milk, sesame seeds and salt and pepper in a mixing bowl.
Drop by spoonful onto the top of the stew, about a 1/4 cup each. Let cook for 10 minutes uncovered, then 10 minutes covered.
Spoon dumplings onto a plate and reserve. Serve up the stew and top with dumplings.