start with two fully-charged hourglasses, it only takes nine minutes.

t=0: start both hourglasses and the egg.
t=4: H#4 runs out. Flip it.
t=7: H#7 runs out. Flip it.
t=8: H#4 runs out again. Flip H#7, which now has 1 minute in the top.
t=9: H#7 runs out.
enjoy ur egg.