Preheat the broiler, place an oven rack at the center of the oven.
Place the potatoes in a medium pot and cover with cold water. Bring to a boil, salt the water and cook until tender, 12-15 minutes.
While the potatoes are cooking, place a large skillet over medium-high heat with about 1 tablespoon of EVOO. Add the chicken, season it with salt and pepper and cook until golden brown and cooked through, 6-7 minutes. Remove the chicken from the pan to a casserole dish, add a drizzle of EVOO to the pan, then add the carrots, peas, and scallions. Season the veggies with salt and pepper and cook until tender, about 2 minutes.
Scoot the vegetables over to one side and melt in the butter. Sprinkle the flour over the butter and cook for about 1 minute, stirring. Whisk in the white wine, cook 1 minute, then whisk in the chicken stock and cook for 1 minute to thicken. Season the sauce with mustard and tarragon then salt and pepper to taste. Pour the sauce and vegetables over the chicken in the casserole and combine.
Drain the potatoes and return them to the hot pot, then mash with the herb cheese, egg yolks, parsley, milk or chicken stock, salt and pepper. Spread the potatoes over the chicken in the casserole dish.
Put the dish under your broiler until the top is golden brown, 3-5 minutes. Garnish with paprika.