Seems like if you burn food in enameled cookware, on very high heat, you will leave a layer of speckled grey/brown marks, which nothing appears to remove.
There are lots of discussions on this board about how to clean enameled cookware (Le Creuset, etc). However none has ever worked without damaging the pan, or gets close enough to a "new" look. I have even thrown out enameled pans in frustration.
Today, I stumbled upon a fail-safe and cheap solution.
1. Wash as well as possible with soap and water until it seems nothing more can be done.
2. Fill with water and 3 heaping spoons of baking soda, and put on max heat. Allow to boil for 30mins or more, and replace water if it gets dry. Never let it dry.
3. Turn off heat, and let sit overnight.
4. Next day, repeat step 2. You may have seen some improvement at this point. But it's not perfect.
* It's possible replacing baking soda with anything else (detergent, vinegar, bleach) might work. Perhaps water alone will be fine until this step.
1. Now remove from heat, empty the water.
2. Make a paste with 1 spoon baking soda and a few drops water, and rub hard with a cloth. The pot/pan will still be HOT, so be careful. You should see it working, now.
*Rubbing the baking soda while the enamel is hot/warm seems to be critical for it to work. I guessed this was the case, because if I burn food and immediately scrape at it, those areas will remain without burn marks. Seems like burn marks gets much harder to remove when cold.
In my case the pan came out like new, and did not use bleach or any other hard chemicals. I forgot to take a "before" picture, but below is the "after" picture.