1. Crack each egg into a custard cup or small bowl.
2. In a medium saucepan, bring 4 cups water to a boil.
3. Add the lemon juice, followed by the eggs, then remove the pot from the heat and cover.
4. Let stand for 7 to 10 minutes, depending on how you like your eggs.
5. Remove the eggs with a slotted spoon.
6. Meanwhile, heat the oil in a medium skillet over medium-high heat.
7. Add the garlic and cook for 30 seconds. Add the broccoli, salt, and pepper, to taste.
8. Cook, tossing occasionally, until tender, 7 to 10 minutes.
9. Divide the broccoli between two serving plates.
10. Top each plate with 2 poached eggs. Sprinkle lightly with salt and pepper.