01 - Preheat oven to 400°F.
02 - Place potatoes in a large pot and cover with salted water. Bring to a boil, reduce heat, and simmer until potatoes are tender, about 15 minutes. Drain thoroughly, then mash with butter, milk, sour cream, salt, and pepper until smooth and creamy. Adjust milk as needed for a soft consistency. Set aside.
03 - Heat olive oil in a large skillet over medium-high. Add chicken pieces, season with salt and pepper, and cook until lightly browned and fully cooked, 5 to 6 minutes. Transfer chicken to a plate.
04 - In the same skillet, add chopped onion and cook until softened, about 3 to 4 minutes. Add garlic and continue cooking for 1 minute.
05 - Pour in chicken broth and bring to simmer, scraping up browned bits. Whisk in Dijon mustard and heavy cream. Simmer until slightly thickened, around 3 minutes. Stir in tarragon if using.
06 - Return chicken to skillet and gently toss to coat in sauce. Remove from heat.
07 - Evenly distribute chicken and sauce in a greased 9x13-inch baking dish.
08 - Dollop mashed potatoes over the chicken mixture and gently spread to fully cover. Sprinkle Gruyère cheese evenly on top.
09 - Bake uncovered for 20 to 25 minutes, until the surface is golden and bubbling.
10 - Allow casserole to rest for 5 minutes after baking. Garnish with chopped parsley before serving, if desired. Serve warm.