How do I get rid of dark brown rings around the gas burners on my stov

have you tried bar keepers friend or bon ami

I like 'BonAmi' won't scratch, and a Mr. Clean Eraser or a 'Green Scrubby' --- and once you get the burned material off -- clean it every week to keep it off

You don't mention what you have tried. My best experience with any stove has been with a baking soda paste and/or Barkeeper's Friend. You may need steel wool if it is really crusty.

Did you try a Mr. Clean heavy duty white sponge?

First you want to remove the "spiders" soak them in very hot water and Dawn dish soap, wait till the water cools down and scrub with a brush or green scrubby and rinse. For the stove top, try soaking it with a cloth soaked in very hot water and ammonia... be sure and cover the center element where the flame comes from as they might be aluminum and the ammonia might discolor it. Use a Mr. Clean Magic Eraser, green scrubby, or Brillo pad to loosen up the stuff... you may have to do it in 'layers' if it has been there a while.... rinse really well... or you will just start the "accumulation" process all over again.

In addition to the excellent suggestions from Landsharkinnc, oven cleaner is formulated to remove the carbonized grease you have described. It won't hurt the porcelain finish on your range.

did you try oven cleaner