Preheat oven to 350°F (177ºC).
Melt butter (3 tablespoons) in a large, high-sided skillet over medium-high heat. Add the onion (1 cup), carrots (1 cup), celery (¼ cup). Cook, stirring often, until vegetables are tender, about 15 minutes.
Sprinkle flour (⅓ cup, plus 2 tablespoons) over vegetables stirring constantly, until the flour coats the vegetables. Cook for 1-2 minutes to toast the flour. Remove skillet from heat.
Return pan to medium-high heat, and whisk in chicken broth (2 ½ cups), and dissolved Better Than Bouillon (1 heaping tablespoon) with water. Bring to a boil, stirring up any brown bits on the bottom of the pan. Cook, stirring constantly, until mixture thickens, about 2 minutes.
Stir in Worcestershire sauce (1 teaspoon), sherry (2 tablespoons), half-and-half (1 cup), salt and pepper to taste, poultry seasoning (½ teaspoon), thyme (¼ teaspoon), sage (¼ teaspoon), garlic powder (¼ teaspoon), frozen peas (1 cup), frozen onions (1 cup), and chicken (4 cups) and simmer a few minutes to heat through.
In a large mixing bowl, stir together biscuit mix with milk and cheese. Stir just until there are no more dry spots. Set the seasoning packet aside.
Using a large spoon, drop the biscuit mix by heaping spoonfuls over the top of the chicken filling. Bake for 14-18 minutes or until the edges are bubbling and the biscuits are cooked through.
In a small bowl, mix together the seasoning packet that came in the box with the biscuit mix and the butter. Brush the top of the pot pie with the seasoned butter. Serve immediately!
