1. Heat vegetable oil over medium-high heat, add chicken and mushrooms. Cook 4 minutes per side. Meanwhile, mince garlic and cut lemon in half. Squeeze juice from half of lemon into a medium-size bowl. Stir in garlic, broth, soy sauce, sugar, ginger, sesame oil and salt. When chicken is golden brown, pour in broth mixture. Bring to a boil, then reduce heat to medium-low. Cover and simmer, turning chicken occasionally, until chicken is springy when pressed, 8 to 10 minutes.
2. Prepare asparagus, broccoli or snow peas. Cut onions into 2-inch- long pieces. In a small bowl, stir cornstarch with water until dissolved.
3. When chicken is done, remove to a platter and cover loosely with foil to keep warm. Bring sauce to a boil over high heat. Stir in vegetables. Stir often until tender-crisp, 3 minutes for asparagus and broccoli or 1 minute for snow peas. Stir cornstarch mixture into sauce. Add green onions. Squeeze in juice from remaining lemon half. Stir constantly until sauce is thickened, 2 to 3 minutes. Pour sauce over chicken. Great with wild rice.