Combine flour mixture in a gallon sized zipper bag. Add chicken drumsticks to bag and seal zipper. Give a good shake to get each piece evenly coated with the flour mixture.
Start water boiling for potatoes (salt if desired)
Add oil to large saute pan over medium high heat. Once hot, add floured chicken pieces (DO NOT DISCARD FLOUR MIXTURE!). Cook on all sides until you no longer see pink - does not need to be cooked through, just browned. Remove from pan. Reduce heat to medium.
In same pan, add butter. Once melted, add onions and saute for 3 minutes. Then add remaining flour mix to pan and whisk together. Let cook 3 minutes then add bouillon powder, and tarragon. Whisk in chicken broth slowly. Let cook another minute then whisk in one cup of heavy cream. Once combined, return chicken to pan and coat with gravy. Reduce heat to medium-low and cover with lid. Let cook for 30 minutes.
Add potatoes to boiling water. Once fork tender (about 25 minutes, depending on size of potatoes), drain in a colander and transfer to large mixing bowl. Add remaining heavy cream, salt, pepper and melted butter. Mash together until desired level of smoothness.
Check that chicken in cooked through with a meat thermometer (should be at least 165degF at thickest part of drumstick).
Serve chicken and pan gravy over top of mashed potatoes. Garnish with parsley if desired.
Keyword Chicken, chicken and potatoes, chicken drumsticks, drumsticks, gravy, mashed potatoes, pan gravy, pan sauce, potatoes, smothered chicken, taragon