hardened residue after high heat cooking (carbon steel and cast iron)
Your residue looks like burnt on carbohydrates to me. It can happen with both sugar and bread, but bread gives it a different shape, it chars in a crumb-like texture. Yours seems like viscous caramel flowed until it burnt on. 

The seasoning of a young pan is indeed quite sensitive. Don't make sticky stuff in it. 

What I have found to work well in new pans is meat with sufficient amount of fat, such as marbled chops or steaks. You also need to do some decent deglazing after that, to remove the stuck-on meat. 

If you get protein residue, make something with wet eggs to clean it. Crepes work great for leaving you with mirrorlike pan seasoning. Use a little bit of oil between every 2-3 crepes. If you can do good scrambled eggs or an omelette, this is also a good pan "cleaner", and the residue taste fits better. But if you are likely to dry out the eggs, it can happen that they take off the not-yet-settled seasoning with them. 

Wet carbohydrates (such as the flour in crepe batter) are no problem, but once dry carbohydrates burn on, I don't know of any method to remove them without damaging the seasoning (and sugar syrup counts as a dry carbohydrate if it stays for long enough to caramelize). Just don't use them on new pans. Once your pan is seasoned well with use, you can start using them, but always combine them with sufficient fat - you should be shallow frying the items which have them, not grilling. 

The oil which you used for seasoning also matters. I've seen lots of sources to recommend flax and other unsaturated oils, because they polymerise easier. The problem is that they are also stickier after polymerisation, especially if the polymerisation wasn't complete. Try seasoning with something which has a larger percentage of saturated fat (lard, coconut oil) and cooking with it the first few times. If you are doing a multi-layer seasoning, you can start the first one or two layers with flax, for a better grip between polymer and metal, but seal it with a saturated oil. 

If you cannot physically remove the caramel residue but want to strip the seasoning and start anew, remove it chemically. Use a strong base, I prefer a lye soak. Don't use acid, it will rust the pan in seconds. You can also leave it there, but it will reduce the evenness of heat transfer and increase the chance that the new seasoning flakes off.