Mix 175g flour and salt in a bowl, then rub in 45g diced butter and 50g lard.
Stir in approximately 4 tablespoons of cold water to bind the dough.
Wrap the dough in film and chill in the fridge for 15 minutes.
Preheat the oven to 220°C.
Simmer chicken with half the onions and bay leaf in water for 45 minutes.
Remove chicken to cool and boil the remaining liquid for 30 minutes to reduce by half.
Shred chicken meat into a 20x30cm pie dish.
Sauté the remaining onions in oil and butter, then stir in 2 tablespoons of flour and mushrooms.
Mix in the reduced stock, wine, and cream, then simmer until thick.
Pour sauce over chicken, add tarragon, and cover with rolled-out pastry.
Brush with beaten egg and bake for 35 minutes until golden.
Cook carrots in butter, sugar, and 5 tablespoons of water, then add peas until glazed.
Serve the pie hot with the glazed carrots and peas.