That's a big asteroid: It's had to dump more than the gravitational binding energy into the moon.

So, the result is 100 km sized chunks of rock flying in all directions. Over time, some will reform a smaller moon, orbiting around a sterile, dead, cratered Earth.

That's because some of the others will hit Earth. Hard. It'll be (briefly) a more intensive period of crater forming since Late Heavy Bombardment. It won't quite boil the oceans and yet it'll wipe out anything more complex than bacteria.