More of this: Giving baked-on Bolognese a hot-towel treatment.
Less of that: Using potentially abrasive cleansers.
The longer spills sit on a stovetop, the more likely they are to fossilize and become a permanent exhibit. Since stove surfaces are prone to scratching when scrubbed, saturate a few cloths in hot water and lay them flat on the stovetop (remove the burners first). Let sit for 10 minutes, then wipe off the softened grime with the cloths (two hands at once!).