Pre-heat a large skillet over medium heat. Cook the bacon strips until all the fat has been rendered out and the bacon is crispy. Remove the bacon from the pan and finely chop.

Toss the breadcrumbs into the skillet and fry in the bacon fat until lightly browned (they will get more brown as the eggs cook). Return most of the chopped bacon to the pan and toss together.

Push the bacon breadcrumbs around in the pan to create four holes in the crumbs. Crack an egg into each of the holes and cover with a lid. Fry the eggs over medium-low to medium heat until the white has cooked through.

While the eggs are cooking, scatter the arugula onto two plates.

Place the cooked eggs in crumbs on the arugula, sprinkling any leftover crumbs on top. Drizzle the sherry vinegar or lemon juice over the top of everything and serve immediately.