Add olive oil to a large deep skillet that has a lid. Add minced garlic and cook until fragrant.
Add the chicken broth and broccoli; cover and cook over a high heat for exactly 4 minutes. Reduce the heat to medium and cook for an additional 3 minutes. Do not remove the lid during cooking. When the broccoli is done, it will be cooked to crisp-tender. If you prefer it a bit softer, remove it from the heat and allow it to sit, covered, for another minute or two.