In a large pot add the chicken breast, bay leaf, and enough water to cover.
Bring to a boil and then reduce to a simmer.
Cook the chicken until fully cooked and tender. Add more water if needed.
Meanwhile, wash peel and dice the veggies.
Heat a large pan or Dutch oven, to medium-high.
Add in the butter and oil.
Add in the onion and stir until just start to soften.
Add in the celery and stir to soften.
Add in the carrots, parsnip, and potatoes. Stir and fry to add colour and soften the veggies.
Stir in the mushroom and tarragon. Fry along with the veggies until cooked down and starting to colour.
Remove the cooked chicken from the water to cool slightly. Then shred with two forks. Reserve the water.
Sprinkle the flour over top of the cooked veggies and stir to coat.
Pour about 3 cups of stock (or use the reserved hot chicken water) into the veggies. Stir to combine and thicken with the flour.
Allow the mixture to simmer as the sauce thickens.
Stir in the shredded chicken. Reduce the heat to low.
Once the sauce is thickened and the the veggies are tender, salt and pepper to taste.
Place the mixture into an oven proof dish.