Meanwhile, in 12-inch skillet, melt 3 tablespoons of the butter over medium-high heat. Add mushrooms and remaining 1/2 teaspoon salt; stir to coat. Cook 12 to 13 minutes, stirring occasionally, until mushrooms are very tender and skillet is nearly dry. Stir in remaining tablespoon of garlic and the thyme; cook about 1 minute or until garlic is fragrant. Add 1/2 cup of the wine, stirring occasionally to deglaze skillet, and cook about 3 minutes or until most of the wine is absorbed. Stir in remaining 1/2 cup wine and the broth. Heat to simmering; cook 2 to 3 minutes or until liquid has reduced slightly. In small bowl, mix remaining 1 tablespoon butter and the flour; mash with fork to form a paste. Beat butter mixture into wine mixture in skillet using whisk. Simmer about 3 minutes, beating constantly, until paste is completely dissolved and mushroom sauce has thickened. Add meatballs to skillet; gently stir to coat. Garnish with parsley.