Heat the oven to 425°F.
Heat the oil and 2 tablespoons of the butter in a large oven-safe skillet over medium-high heat. Add the chicken and cook for 2 minutes.
2 tablespoons neutral oil, 3 boneless skinless chicken breasts
Add the onion, carrot and celery with a pinch of salt. Cook for about 5 minutes to sweat the vegetables.
1 cup onion, 1 cup carrots, 1 cup celery, 1 pinch salt
Add the garlic and sauté for 3 more minutes, until the onion is translucent.
4 cloves garlic
Add the butter. Sprinkle in the flour and stir for 1 to 2 minutes to make a roux.
4 tablespoons butter, 4 tablespoons all-purpose flour
Pour in the white wine and stir for 30 seconds. Add the bouillon paste, water and cream, and stir until smooth.
½ cup dry white wine, 2 teaspoons chicken bouillon paste, ½ cup water, ½ cup heavy cream
Simmer on low, stirring often, until the sauce thickens and the chicken is cooked through, 5 to 8 minutes.
Stir in the frozen peas at the very end and turn off the heat.
1 cup frozen peas
Cut the puff pastry into small squares. Arrange them over the filling, overlapping each other. Brush the egg wash over the pastry.
1 sheet puff pastry, 1 egg
Bake at 425°F for 25 to 30 minutes, until the pastry is puffed and deep golden and the filling is bubbling. Let it rest for 5 minutes before serving.