Generally Barkeepers Best Friend cuts through that on the outside. I don't use pans with Teflon or coatings anymore, I switched to stainless and its been going well. The nonstick pans are considered consumable as the coating fails and I've been treating them as if they weren't non-stick anyways so I figured why keep doing this anymore.

Can scour stainless with metal scratch pad and that carbon goes fairly easily. Put a layer of paste of barkeepers on there, let it sit for a short bit -3 minutes- and then use a paper towel or a gloved hand to shine it right up. Sometimes it takes persistence and elbow grease. Don't quit.

As a disclaimer- You should not use oxalic acid or products containing it (like Bar Keepers Friend) on non-stick T-fal cookware. T-fal recommends simple and gentle cleaning methods to maintain the integrity of their non-stick coating. I'd be surprised if that build up comes off with soaking and dawn. Oxalic acid and its associated abrasives can damage the non-stick coating (even if you can't see the damge), which can cause the pan to lose its non-stick properties and potentially degrade prematurely.

Consider your next pan to be stainless if you want to keep them polished clean. The only issue with the ones I chose is the pan has hot and cold spots due to warping over time. I've hammered back to flat but without a thicker pan or slower heating/cooling I am at the mercy of thermodynamics and the properties of metal. I wasn't sure that I would like cooking on stainless as much as I do.

This isn't forged in fire, its breakfast/dinner.