Start with sifting your flour and salt into a medium sized bowl, then add butter to bowl. Break butter down with your fingers to combine with the flour. Place bowl in the fridge for 15 minutes.
Whisk egg yolk and butter together. Take flour and butter out of the fridge and add in the egg yolk mixture. Knead the dough with your hands until you form a dough ball. Wrap your dough ball in saran wrap and place in the fridge until you are ready for it.
Heat up saucepan over medium heat, then melt butter in the pan. Add onions, celery, carrot, and garlic to the butter. Cook for a few minutes until onions are translucent and veggies are cooked through.
Whisk together cornstarch and 1 cup of broth to create a slurry, then pour into the veggies. Let simmer until sauce thickens, then pour in the remaining chicken broth.
Add remaining thyme and chicken to the pan. Season with salt and pepper to taste. When the sauce has thickened, ladle your chicken mixture into 4 ramekins.
Remove dough from fridge and let it get to room temperature. Roll dough out to ⅛ inch thick and cut 4 circles to cover the ramekins. Cut an “x” into the top for air to get out.
Brush your crust with egg wash, then bake at 375 degrees F for 40 minutes. Serve hot!