Heat 1 teaspoon of oil in a large pan over medium heat. Add the asparagus and mushrooms and cook for 2-3 minutes or until just tender.
Add the garlic to the pan and cook for 30 seconds more.
Remove the vegetables from the pan and place on a plate. Cover the plate with foil to keep warm.
Add the remaining tablespoon of oil to the pan.
Season the chicken with salt and pepper and add it to the pan. Cook the chicken, stirring occasionally, until browned and cooked through, 3-4 minutes per side
In a bowl whisk together the oyster sauce, chicken broth, honey, sesame oil, and soy sauce. In a small bowl mix the cornstarch with a tablespoon of cold water.
Add the vegetables back to the pan.
Pour the oyster sauce mixture over the chicken and vegetables; cook for 30 seconds. Add the cornstarch and bring to a boil; cook for 1 more minute or until the sauce has just started to thicken.
Top with sesame seeds and serve immediately.