Heat the oven to 400Β°F (200Β°C). Pat the chicken dry and season with 1 tsp kosher salt and 0.5 tsp black pepper.
Heat the olive oil in a large, deep skillet over medium-high heat. Add the chicken in a single layer and cook until lightly golden on the edges, 5β7 minutes. Transfer to a plate, leaving any juices in the pan.
Add 2 tbsp of the butter to the skillet. Stir in the sliced mushrooms and cook, stirring occasionally, until browned and their liquid has evaporated, 6β8 minutes. Transfer to the plate with the chicken.
Reduce the heat to medium and add the remaining 2 tbsp butter. Add the onion and cook until translucent and sweet, 4β6 minutes. Stir in the garlic and cook until fragrant, 30 seconds.
Sprinkle the flour over the onions and cook, stirring constantly, until the flour smells nutty, 1β2 minutes. Pour in the white wine and stir, scraping up any browned bits; simmer until mostly reduced, 1β2 minutes.
Gradually whisk in the chicken stock until smooth. Add the bay leaf and thyme and simmer, stirring often, until thick enough to coat the back of a spoon, 5β7 minutes.
Stir in the heavy cream. Return the chicken and mushrooms (and any accumulated juices) to the pan and simmer gently until the chicken is just cooked through and the sauce is silky, 5β7 minutes. Remove and discard the bay leaf. Season with the remaining 0.5 tsp kosher salt and 0.5 tsp black pepper. Let the filling cool until barely warm, 20β30 minutes.
Transfer the cooled filling to a 9-inch pie dish (or 1.5β2 quart baking dish). On a lightly floured surface, roll the chilled puff pastry to about 1/8-inch thick to fit the dish with a slight overhang. Lay the pastry over the filling, trim, and crimp the edges to seal. Cut 2β3 small slits in the top for steam.
Brush the pastry evenly with the beaten egg. If desired, decorate with pastry trimmings and brush again.
Bake until the pastry is deep golden and the filling bubbles at the edges, 25β30 minutes. Let the pie rest 10 minutes before serving so the sauce sets.