Cook the Bacon: Place a large, non-stick frying pan over a medium heat. Lay the bacon rashers in the cold pan and let them cook, turning occasionally, for 8-10 minutes or until they reach your desired level of crispiness. Remove the bacon to a plate lined with kitchen paper and set aside. Carefully wipe the excess fat from the pan.

Prepare the Bread: Lay the four slices of sourdough on a chopping board. Spread the softened butter or mayonnaise evenly over one side of each slice. On the unbuttered side of two slices, spread the Dijon mustard, if using.

Assemble the Sandwich: Flip the two mustard-spread slices over. Divide half of the grated cheese between them. Top with the cooked bacon rashers, breaking them if needed to fit. Sprinkle the remaining cheese over the bacon.

Toast the Sandwich: Place the remaining two slices of bread on top, buttered-side-up. Carefully transfer the sandwiches to the frying pan over a medium-low heat. What works best for me is pressing down gently with a spatula for the first minute to ensure great contact with the pan and even browning.

Cook Low and Slow: Cook the sandwiches for 4-5 minutes on the first side, until the bread is a deep golden brown. Carefully flip them over and cook for another 3-4 minutes on the other side, until golden and the cheese is completely melted and oozing.

Fry the Eggs: While the second side is toasting, use a separate small pan to fry your eggs to your liking. A sunny-side-up egg with a runny yolk is traditional and adds a wonderful sauciness to the sandwich.

Serve Immediately: Once the grilled cheese is ready, transfer it to a chopping board. You can either place the fried egg on top or gently open the sandwich and place it inside. Slice in half with a sharp knife and serve straight away while it's hot and the cheese is stretchy.