Lodge Manufacturing Company CRS12HH61 Carbon Steel Skillet, 12", Black/Orange
Plus one for the Bar Keepers Friend. If you don't have any and don't want to buy it, you can also soak the pan in white wine vinegar and scrub it again. I sometimes use a little fine steel wool or an SOS pad on my All-Clad pans when I have a baked-on grease stain like this. I'm interested to see if others ever use steel wool or not on their All-Clad or other stainless steel pans.
You can also put some water in the pan and bring to a boil for a few minutes. Shut off and mix in some dish soap and let it soak for a couple of hours then scrub.
Don't worry though, if you work at it a bit, one way or another it will come off.
OP, as far as your question about 5 minutes of high heat, every situation is different. The All-Clad pan can handle the heat itself but whatever combination of heat and probably a very light amount of oil was just right to scorch some stains on the pan. The All-Clads have great distribution of heat so maybe you don't need the heat as high as you had it. Sometimes your heat source, electric, gas or induction might be different from what you are used too and it may have heated the pan more than you thought. Most likely, whatever combination of tortillas and oil you had was just enough to put a very light coating on the pan then cook it practically dry so the residue from the tortillas and oil just baked right on. Maybe a few drops more oil would have kept this from happening or an oil with a higher smoke point. Maybe you didn't use any oil at all and all that was there was whatever was in the tortillas. Just offering a few thoughts here. Lastly, if you want to use a high heat to crisp up something like tortillas or, say, left over pizza, I get really good results using a high carbon steel pan or cast iron instead of my All-Clad stainless steel.