Preheat oven to 400°F.

Melt butter in a (10-inch) oven-safe skillet over medium-high heat. Add chopped onion and saute for 2 minutes. Add chicken and sprinkle with salt and pepper. Cook until chicken is browned, about 5 minutes.

Add flour and stir to combine. Slowly add chicken stock and stir to combine. Add in vegetables, thyme, and cheese. Stir to combine, simmer for 10 minutes until liquid is thickened and reduced.

Arrange the puff pastry rectangles on top of the pot pie, overlapping. Brush the tops with the beaten egg, and bake 30 minutes, until the puff pastry is golden brown and lightly puffed.

Let pot pie rest about 10 minutes, and then serve family style with another sprig of fresh thyme on top.