Preheat your oven to 190C. Prepare the chicken by spatchcocking it: flip it over, cut along the ribs to remove the spine, and flatten it. Rub with olive oil and salt, then roast for 30 minutes or until juices run clear. Let it rest.
For the garnish, peel and cut the shallots into chunks, quarter the mushrooms, and slice the lardons. Saute in olive oil until golden.
Remove the meat from the chicken, reserving the carcass and bones. Dice the meat into bite-sized pieces and set aside. Drain and reserve the chicken fat.
For the sauce, roast the carcass and bones at 200C for 20 minutes. Saute sliced shallots and crushed garlic in a pan, add white wine and aromatics, and reduce. Add chicken stock, simmer, and reduce by half. Strain and whisk in cream, then thicken with a beurre manie made from flour and chicken fat.
Stir the chicken and garnish into the sauce. Add chopped parsley and tarragon, season with salt and pepper, and let cool.
Roll out puff pastry to line a pie dish, refrigerate. Roll out a pastry lid, refrigerate. Preheat oven to 180C Fan. Fill the pie dish with chicken filling, cover with pastry lid, and bake for 25 minutes. Remove, brush edges with egg wash, place lid on top, and bake for another 10 minutes. Let stand before serving.