Melt butter with olive oil in a large skillet over medium heat; add mushrooms, salt, and pepper. Cook, stirring occasionally, 12 to 15 minutes or until tender and almost all liquid has evaporated.
Remove from heat. Stir in bourbon or chicken broth; return to heat, and cook 2 to 3 minutes or until slightly thickened. Reduce heat to low; stir in minced garlic, chopped fresh parsley, and chopped fresh thyme. Cook 1 more minute.