Remove chicken from packaging and pat dry with paper towels. Slice into 3/4 inch strips. Season with garlic, salt and pepper and toss to coat well.
Add olive oil to a large skillet and place over medium- heat. When oil is hot, add the chicken and cook for 8-10 minutes, turning to brown on all sides.
Remove chicken to a bowl, reserving olive oil in the pan.
Coarsely chop the onions or slice thin if preferred.
Cook onions over medium heat, stirring occasionally, until well caramelized.
Remove onions and set aside.
Add additional olive oil and butter to the pan with the flour. Whisk together and continue to cook, whisking often until flour mixture is golden brown.
Whisk in the chicken broth, Worcestershire sauce and brown mustard, scraping up the brown bits from the bottom and sides of the skillet.
Add garlic, rosemary, thyme, salt and pepper. Continue to cook, whisking often until sauce is thickened.
Stir in cooked chicken and caramelized onions, cook 5 minutes.
Remove from heat and top with shredded cheese.
Cook under the broiler for about 3- 5 minutes, watching carefully, until cheese is melted and starts to brown.
Remove from oven and garnish with parsley.
Serve over mashed potatoes, pasta or garlic bread.