Dice chicken into bite-sized pieces and boil until cooked through (about 10 minutes).

Melt butter in a skillet over medium-low heat. Add the vegetables, parsley, and thyme and cook 10 minutes.

Preheat the oven to 350°F.

Add in flour and cook 5 minutes, stirring constantly.

Stir in chicken broth and half-and-half and cook until sauce is thick and bubbling.

Add the cooked chicken and turn to coat. Season with salt and pepper.

Pour the mix into a casserole dish and arrange the biscuits on top. Beat together egg yolk and water in a small dish and spread on biscuit tops.

Bake in the oven for 25-30 minutes, or until biscuits are golden brown and mix is bubbling.