Finely slice the red onions, then tip them into a large frying pan with the butter and a big pinch of salt. Cover and cook on a low-medium heat for 30 mins, stirring regularly. Take off the lid, then scatter with the sugar, season well and cook for 5 more mins until caramelised.
Meanwhile, melt the butter in a pan, then whisk in the stout and the English mustard. Stir in the grated cheddar and whisk until melted, then season and add a splash of Worcestershire sauce. Take off the heat, then whisk in the egg. Divide the onions between two toasts, top with dollops of the cheesy sauce, then grill for 2-3 mins until browning and bubbling.