Preheat your oven to 200°C (400°F). Prepare a 23cm x 33cm (9x13 inch) baking dish by lightly greasing it with butter or cooking spray.

In a large skillet or Dutch oven, melt 100g (7 tbsp) of butter over medium heat. Add the finely chopped 1 medium yellow onion, 2 diced carrots, and 2 diced celery stalks. Sauté for 8-10 minutes, stirring occasionally, until the vegetables are softened but not browned. This process builds a flavorful base for the creamy filling.

Sprinkle 75g (1/2 cup + 1 tbsp) of all-purpose flour over the softened vegetables. Stir continuously for 1-2 minutes to cook out the raw flour taste and create a roux. The mixture will become thick and pasty.

Gradually whisk in 500ml (2 cups + 2 tbsp) of chicken broth, followed by 250ml (1 cup) of milk. Continue whisking to ensure no lumps form. Bring the mixture to a simmer, stirring constantly, until it thickens into a rich, creamy sauce, about 5-7 minutes. You are looking for a consistency that coats the back of a spoon.

Stir in the cooked and shredded or diced chicken (750g or 1.65 lb), 150g (1 cup) of frozen peas, 5g (1 tsp) of salt, and 2g (1/2 tsp) of black pepper. Mix well to combine everything. Taste and adjust seasoning if needed. Pour this creamy chicken mixture evenly into the prepared baking dish.

Prepare the biscuit topping. In a large bowl, whisk together 250g (2 cups) of all-purpose flour, 15g (1 tbsp) of baking powder, 5g (1 tsp) of salt, 5g (1 tbsp) of dried parsley, and 2g (1 tsp) of dried thyme. Ensure the dry ingredients are thoroughly combined.

Add the 75g (5 tbsp) of cold, cubed unsalted butter to the dry ingredients. Use a pastry blender, your fingertips, or two forks to cut the butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces of butter remaining. These butter pieces will create flaky biscuits.

Gradually pour in 150ml (2/3 cup) of milk, mixing with a fork until just combined. Be careful not to overmix, as this can lead to tough biscuits. The dough should be shaggy and slightly sticky.

Drop spoonfuls of the biscuit dough evenly over the chicken mixture in the baking dish. You can use about 6-8 large spoonfuls, leaving small gaps between them to allow steam to escape and ensure even cooking. They don't need to cover the entire surface perfectly.

In a small bowl, whisk together 1 large egg and 1 tbsp (15ml) of water to create an egg wash. Brush the tops of the biscuits lightly with the egg wash for a golden-brown finish. This step is optional but adds a nice sheen and color.

Bake in the preheated oven at 200°C (400°F) for 20-25 minutes, or until the biscuits are golden brown and cooked through, and the chicken filling is bubbling around the edges. You can test the biscuits by inserting a toothpick into the center; it should come out clean.

Let the casserole rest for 5-10 minutes before serving. This allows the filling to set slightly, making it easier to serve. Serve hot.