That'll do!
Yet, without having to wait 7 extra minutes to drop egg:
Start both glasses as you start boiling the egg.
After the 7-minute glass runs out, turn it over to start it again.
Four minutes later, when the 11-minute hourglass runs out, turn the 7-minute glass again.
Wait for the 7-minute glass to run out, which will take another 4 minutes and get you to exactly 15 minutes of boiling time.