Combine chicken, 1 teaspoon cornstarch, 1/4 teaspoon salt, and pepper in a medium bowl; set aside.
Combine oyster sauce, water, sugar, remaining 2 teaspoons cornstarch, and remaining 1/4 teaspoon salt in a small bowl; set aside.
Heat oil in a large nonstick skillet over medium-high heat. Add chicken mixture and garlic; sauté for 3 minutes. Add snow peas and mushrooms; sauté 2 minutes. Stir in broth; bring to a boil. Stir in oyster sauce mixture; cook for 30 seconds or until thickened. Stir in onions; remove from heat.