Carbon steel should not have any non-stick coating applied from factory. Using a pure carbon steel pan will create a slick surface. Look at e.g. DeBuyer for a g

Carbon steel should not have any non-stick coating applied from factory. Using a pure carbon steel pan will create a slick surface. Look at e.g. DeBuyer for a good brand. In your case I think that oil gets over the lip and around the pan.