I don't think scraping with a razor blade or an abrasive cleanser will work.  It's metal with baked on enamel(I assume).  It is not a flat top.  
I'm currently trying the wet paper towel experiment.   
 
 
Is the bar keeper's friend abrasive?
I really do hate this stove.  It has a "power" burner which heats things up quicker, but the enamel gets terribly hot and causes these impossible to remove spots. 
I tried lining with aluminum foil and it didn't work because somehow I was blocking the gas flow.  
I need to get some pre-formed square liners.  Anyone seen them at a convenient (north chicago) location?
The rice pudding recipe, btw, was from The New Best Recipe from Cook's Illustrated.  It was good the first day.  By the second day, I had probably eaten to much if it by then, however the consistency was wrong: cold and gloppy.   At room temperature it was still gloppy.
                    
                        
                            
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