Normally we love funk, but not THIS kind of funk

funk alla that... if chemicals are not an option, you're gonna most likely need an impliment of destruction such as a razor - or metal scraper - like a spatula. i know that mine is also a black enamel, and stands up to the cleaning abuse. but i agree with ivy. avoid the poison and clean often.

Since it's a flat surface, I would put the Bar Keeper's Friend on it, then a few paper towels (about 4), and then pour some boiling water on the paper towels, careful to only pour enough water that the paper towels will hold, and let it sit for about 15 min, then wipe it off, and repeat as necessary. -- good luck

Usually if it's a small spot I'd just fold a paper towel in fourths.

I've had the normal gas and glass top, vinegar worked well with both.

Margaret- I'd try steel wool on a small area first. You're talking about the grates that hold your pans up on a gas stove right? I think steel wool would be okay on those.

I use vinegar spray for everything from the kids' plastic table to the flattop stove.

If it's really bad, use dishwasher powder straight from the box as scouring powder. Use hot water and a nylon scrubbie.

Kendra, are you recommending vinegar spray for all cooktops or specifically the glass ones?
NOT that my stovetop is dirty or anything, ahem.
What I find hardest to clean are the grates that sit over the burner (not sure if they have a specific name - you know, the thing the pans sit on). I've soaked and scrubbed, but I guess I didn't actually use B-K Friend. Could I use steel wool??

I find that a razor blade kit made for glass tops work well too. No elbow grease involved. A daily wipe up with vinegar spray and it stays looking new.

You can also clean that up with a paste made from baking soda & water. Will definitely need some elbow grease and several applications, but it will come up.