Add the olive oil to a nonstick pan over medium heat. Once it's heated add the minced garlic. Let the garlic cook for 1 minute, then pour in the chicken broth.
Stir in the Dijon mustard and half and half, then bring to a simmer.
In a small bowl, add the cornstarch with a couple tablespoons of water. Whisk the cornstarch mixture into the pan. Whisk occasionally until it starts to thicken.
At this point, you can stir in the chicken, thyme, salt, and pepper.
Serve by itself, over rice, or with noodles.