For the filling, in a large skillet, melt 2 Tbsp. butter over medium high heat. Add carrots, onions and red pepper. Cook for 5 minutes, stirring occasionally.
Add the mushrooms and season with 1/2 tsp. salt and 1/4 tsp. pepper and cook for 5 minutes until lightly browned.
Add the garlic and and thyme and continue to cook for 1-2 minutes until fragrant.
Remove from the heat and stir in the peas. Set aside.
In a large saucepan, melt the remaining 4 Tbsp. butter over medium-low heat.
Add the flour and whisk constantly for 1 minute.
Whisk in the white wine and continue to cook for 1 -2 minutes until almost evaporated.
Gradually add the cream and the stock. Raise the heat to medium-high, and bring to a boil.
Reduce heat to low and simmer until thickened, stirring occasionally.
Stir in the vegetables and the chicken and season with remaining 1/2 tsp. salt and 1/4 tsp. pepper and parsley.
Remove from heat.
Preheat oven to 400 degrees.
Spoon chicken mixture into 6 individual ramekin dishes.
Dust puff pastry sheets with flour and roll out to 1/4 inch thickness. Place ramekin on top of sheet and cut a square about 1/2 inch larger than the circle all around to make six squares. You can also opt to top each ramekin with a circle of puff pastry the same size as the top of the ramekin (as pictured).
Cover each bowl with the puff pastry pressing a little at the edges, cut 3 small slits in the middle of the puff pastry with a sharp knife to let steam escape, then brush the tops with the egg wash.
Bake at 400 degrees for 30 minutes, until bubbly and golden brown. If puff pastry starts to get too brown, tent loosely with a piece of foil.
Transfer to individual plates and serve.