Then I just wipe that crud off with a paper towel.
All those little burned-on spatters and the stuff that gets under the burner just wipe right off. I have no clue as to how it gets under there. It seems to defy the law of gravity by moving under a solid object. Back to topic.
After I get the melted crud wiped off, I switch to a dishcloth and LOTS of water. Fill your sink with warm water. Wipe, rinse the cloth, wipe, rinse. Keep going until all the Easy-Off is, well, off. If you find any stubborn bits, use a green scrubby. Now you have a shiny clean stovetop:
There's a quick way to clean the burned-on spatter off of your grates and burners too: The self clean cycle on your oven. Leave the oven racks in there and place your stove burners and grates on the oven racks. Set it to self clean. When the cycle is done and the oven has cooled, your grates and burners will have a fine coating of grey ash. Rinse in your sink, dry and replace.
*Disclaimer. This use is totally off-label. Try it on a tiny section first. I wouldn't use for anything other than a gas burning, porcelain stove top. Other stove surfaces have their own particular cleaners - use them.