Heat a large skillet over medium heat. Add butter. Once melted, add mushrooms and carrots. Cook for 5-8 minutes or until carrots are soft. Stir in fresh thyme and cook another minute. Add flour and continue cooking a minute longer. Slowly pour in wine and milk, whisking to ensure that no clumps form in sauce. Bring sauce to a low boil. Reduce heat and stir in cayenne pepper, peas and cooked chicken. Simmer sauce for 5 minutes or until thickened. Remove from heat and let cool. Stir in the Parmesan cheese.