Prep. Heat oven to 350°F.
Saute. Melt butter (3 tablespoons) in a large, high-sided skillet over medium-high heat. Add the onion (1 cup) and carrots (4). Cook, stirring often, until vegetables are tender, about 15 minutes. Sprinkle flour (1/3 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.
Broth. Return pan to medium-high heat, and whisk in chicken broth (2 1/2 cups), and dissolved Better Than Bouillon (1 heaping tablespoon). 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), half-and-half (1 cup), salt, pepper, poultry seasoning (1/2 teaspoon), thyme (1/4 teaspoon), sage (1/4 teaspoon), frozen peas (1 cup), frozen onions (1 cup), and chicken (1) and simmer a few minutes to heat through.
Assemble. Transfer chicken and vegetable mixture to a 9X13 inch baking dish. Arrange biscuits on top of the filling.
Bake in the preheated oven for 25-30 minutes or until the casserole is bubbly and the biscuits are cooked through. If the biscuits need more color, place them under the broiler for 2-3 minutes or until the biscuits are nicely browned.