Use chef’s knife to cut chicken breasts crosswise at an angle, in thin strips.
In medium bowl, whisk 1 tablespoon water, soy sauce, cornstarch, and baking soda until combined.
Add sliced chicken to bowl with soy sauce mixture. Wash your hands. Use rubber spatula to stir to coat. Let chicken sit for 15 minutes.
While chicken sits, in second medium bowl, whisk hoisin sauce, chili-garlic sauce, and remaining ¼ cup water until combined.
When chicken is ready, heat oil in 12-inch nonstick skillet over medium-high heat for 1 minute (oil should be hot but not smoking). Use rubber spatula to carefully add chicken to skillet and spread it into even layer. Cook, stirring occasionally, until chicken is lightly browned on both sides, 2 to 4 minutes. Turn off heat and use rubber spatula to transfer beef to large plate.
Add hoisin mixture, broccoli, and garlic to skillet and return to medium high-heat. Cook, stirring occasionally, until sauce is thickened and broccoli is tender, about 5 minutes.
Stir chicken and juices on plate back into skillet and cook for 1 minute. Turn off heat. Serve.
