Melt butter in an oven-proof skillet on medium-high heat. Add onion; cook and stir until tender, about 3 minutes. Add garlic; cook another minute.
In a large bowl, mix flour, broth, milk and pepper until smooth. Pour into skillet and bring to a boil, stirring continuously. Continue cooking and stirring for 2 minutes until thickened. Add the turkey, peas and carrots and fresh thyme and heat through. Arrange quartered biscuits over stew. Bake until biscuits are golden brown, 15-20 minutes. Sprinkle on fresh parsley, if desired.