I doubt if it's at all possible to bring it back to its original new state Kat.
What you can do is to fill the damaged area with something like Araldite........ better still would be this ..................
It's made by Unibond, and it has the advantage of being heatproof.
You'd have to colour the repair with a touch-up paint, preferably a high-temperature product.
its the chipping and the cracks - and kids don't help; mind you an electrician dropping a 30kg ice maker on it didn't do it any good and he had to replace it - he was fixing a dead-man's switch underneath as our kids were young at the time...thought he was doing us a favour by repacking the space under the hob when he slipped a little and dropped it.
my children - 3- were quite young when I bought the first one - so they've grown up with 'em - when I say I've had several that is because of house moves.
Oh - and as for speed - this induction ceramic hob - fitted recently - is wonderful