Cook onion, mushrooms, and carrot. Melt butter in a large skillet over medium heat. Add onion, mushrooms, and carrot. Cook 5-7 minutes until vegetables are softened.
Add flour and cook. Sprinkle flour over vegetables and stir to coat. Cook 1-2 minutes, stirring constantly.
Add liquids. Slowly pour in chicken broth while stirring. Add heavy cream and cook 3-5 minutes until sauce thickens.
Season and add cheese. Season with garlic powder, salt, and pepper. Stir in cheese until melted.
Add chicken and peas. Add chicken and frozen peas, stirring until combined.
Assemble. Pour mixture into prepared casserole dish. Cut each biscuit into quarters and press pieces lightly into the top of the casserole.
Bake. Bake 15-20 minutes until biscuits are golden brown and cooked through. Let cool 5 minutes before serving. Garnish with green onions.