Cooking Toad In The Hole - preventing "burn on"
I grew up in Yorkshire, that doesn't make me an immediate expert but my Mother used lard or beef dripping to coat the container for either Yorkshire Puddings or Toad in the Hole.
You should preheat the lard in the oven, it should be 'very' hot.

I suspect the issue with using the oil from the sausages is that you will get some water as well as the oil. This will not coat the batter and will evaporate quickly. Or the oil is not hot enough when put in the container. I suggest putting the residue from the sausage in a gravy not for the Toad in the Hole.

P.S. I don't know what (from the linked recipe) the sausage chunks means, but keep your sausages whole imo.