Place the chicken breasts in a pot with the quartered onion and one of the bay leaves. Fill the pan with just enough water to come to the top of the chicken breasts. Bring the mixture to a low boil, reduce the heat to a simmer and poach the chicken for 12-15 minutes. Remove the chicken and dice or shred with forks. Reserve the poaching liquid.
In the same pot, heat 2 tablespoons EVOO, a couple of turns of the pan, over medium-high heat. Add the mushrooms and lightly brown. When the mushrooms are just tender, add the remaining two chopped onions, potatoes, parsnips, celery, sage, salt, pepper and the remaining bay leaf. Cover the pot and sweat the vegetables for 10 minutes, stirring occasionally. Remove the bay leaf. Melt the butter in the pot, add the flour and stir to make a light roux. Deglaze the pan with a splash of white wine and add 1-2 cups of the reserved poaching liquid. Whisk in the mustard and 2 cups chicken stock. Add the cream. Thicken to a light gravy consistency. Adjust the salt and pepper and add in the chicken.
Reduce the heat to low and bake off the pastry tops.
For a make-ahead meal: Bake off the pastry tops; cool the filling and store. Reheat the filling over medium heat, covered, to a bubble, then reduce the heat to a simmer.
To prepare the pastry tops: Cut the pastry into shapes that reflect the shape and size of the dishes or bowls you wish to serve the soup in. Beat the egg with a splash of water and arrange the cut pastry on a nonstick baking sheet or a parchment-lined sheet pan. Brush the dough with the egg wash and bake to golden for 12 minutes at 425°F.
Cook’s note: The chicken and mushroom filling can also be served as a thick soup with a crusty, warm baguette for dipping.