Directions

1. Using a small piece of cheesecloth, make a bouquet garni: Wrap 3 garlic cloves, peppercorns, thyme, bay leaf, and parsley stems; tie in a bundle with kitchen twine.
2. Cut chicken into 2-by-3/4-inch strips. In a large, deep skillet or Dutch oven, heat 1 tablespoon oil over medium-high heat. Add onions and remaining 3 cloves garlic; cook, stirring occasionally, until they begin to brown, about 4 minutes. Add mushrooms and cook until golden, about 4 minutes. Transfer vegetables to a medium bowl; set aside.
3. Add butter and remaining 1 tablespoon olive oil to skillet. Season with salt and pepper; cook chicken in two batches until browned, about 1 minute per side. Return all chicken to pan. Add cognac and wine. Use a wooden spoon to scrape up any brown bits from the bottom. Add chicken stock; stir in tomato paste. Add bouquet garni. Bring to a boil; reduce heat to a simmer, and cook, covered, 15 minutes.
4. Using a slotted spoon, transfer chicken to a bowl with reserved vegetables; discard bouquet garni. Cook broth over high heat until reduced by half, about 12 minutes. In a small bowl, dissolve cornstarch in 1 tablespoon cold water. Pour back into broth, and stir until incorporated. Cook 2 minutes. Return chicken and vegetables to pot; cook over medium-low heat until warmed through. Chop parsley leaves, and stir in. Garnish with thyme before serving.