1. Heat olive oil in a large skillet over medium-high heat. Add chicken and cook until lightly brown on all sides, about 5 minutes.
2. Add garlic and cook, stirring, until fragrant, about 30 seconds.
3. Add chicken broth (reserve 1/2 cup for later), soy sauce, sugar and ginger. Cook for 3 minutes.
4. Add broccoli, cover and cook for 8 minutes until crisp-tender.
5. Mix cornstarch with the remaining 1/2 cup broth. Add to the skillet and cook, stirring often, about 3 minutes, until the sauce thickens.