Date: June 17, 1775
Let me set this up a bit: there were two places where rebel forces would have been able to mount attack on British-occupied Boston - one was the Charlestown peninsula to the north, the other was Dorchester Heights, to the south. When rumours started that the British were going to fortify the hills around Charlestown, the rebels decided to act.
By which I mean do something; not put on a little play.
On the night of June 16, 1775, troops under the command of William Prescott sneaked onto the peninsula, occupied Bunker Hill and built fortifications on Breed's Hill. It was a tactically terrible choice - Breed's Hill was easier for enemies to climb, much more open to attack, and close enough to the British ships in the harbour to come under fire. In fact, Prescott's orders were to fortify Bunker Hill - it's uncertain why he made the switch. Maybe he had trouble with B words, like Bunker and Breed's. He probably thought he was fighting against the Belgians, not the Brits.
Fortunately for the rebel army, it seemed the British were almost as tactically inept as they were. When General Howe landed troops at Moulton's Hill, he waited for reinforcements, rather than attacking immediately. This gave the rebel forces time to shore up their fortifications. When Howe finally did attack, he divided his forces, expecting the disorganized rebel army to fall before him - which it didn't. In fact, the British forces attacked and retreated twice before winning the day - after they'd received more reinforcements and the rebels were mostly out of ammunition.
The casualty reports are telling: 228 British soldiers dead, including many of their officers, and more than 800 injured. On the rebel side, 301 injuries and 140 deaths. The Continental Army had shown they could hold their own against the better-trained British Army - and it's hard to say which side was more surprised by that. It still surprises me to this day.